Deck 6: Introduction to Continuous Probability Distributions

Question 1

A continuous random variable approaches normality as the level of skewness increases.

Answer 1

False

Question 2

One example of a difference between discrete random variables and continuous random variables is that in a discrete distribution P(x > 2) = P(x ≥ 3) while in a continuous distribution P(x > 2) is treated the same as P(x ≥ 2).

Answer 2

True

Question 3

Watersports Rental at Flathead Lake rents jet skis and power boats for day use. Each piece of equipment has a clock that records the time that it was actually in use while rented. The company has observed over time that the distribution of time used is normally distributed with a mean of 3.6 hours and a standard deviation equal to 1.2 hours. Watersports management has decided to give a rebate to customers who use the equipment for only a short amount of time. They wish to grant a rebate to no more than 10 percent of all customers. Based on the information provided, the amount of time that should be set as the cut-off between getting the rebate and not getting the rebate is approximately 2.06 hours.

Answer 3

True

Question 4

When graphed, the probability distribution for a discrete random variable looks like a histogram.

Question 5

The State Department of Forests has determined that annual tree growth in a particular forest area is normally distributed with a mean equal to 17 inches and a standard deviation equal to 6 inches. Based on this information, it is possible for a randomly selected tree not to have grown any during a year.

Question 6

The parameters of a normal distribution are the mean and the standard deviation.

Question 7

All symmetric distributions can be assumed normally distributed.

Question 8

The probability distribution for a continuous random variable is represented by a probability density function that defines a curve.

Question 9

When a single die is rolled, each of the six sides are equally likely. This is an example of a uniform distribution.

Question 10

The State Department of Forests has determined that annual tree growth in a particular forest area is normally distributed with a mean equal to 17 inches and a standard deviation equal to 6 inches. If 2 trees are randomly chosen, the probability that both trees will have grown more than 20 inches during the year is approximately .037.

Question 11

Watersports Rental at Flathead Lake rents jet skis and power boats for day use. Each piece of equipment has a clock that records the time that it was actually in use while rented. The company has observed over time that the distribution of time used is normally distributed with a mean of 3.6 hours and a standard deviation equal to 1.2 hours. Watersports management has decided to give a rebate to customers who use the equipment for less than 2.0 hours. Based on this information, the probability that a customer will get the rebate is 0.4082.

Question 12

Typically, a continuous random variable is one whose value is determined by measurement instead of counting.

Question 13

A manufacturer advertised that the time it takes a person to assemble a bookcase has been shown to be normally distributed with a mean equal to 125 minutes with a standard deviation equal to 20 minutes. Given this information, the probability that it will take a randomly selected person more than 105 minutes is about 0.1587.

Question 14

The actual weight of 2-pound sacks of salted peanuts is found to be normally distributed with a mean equal to 2.04 pounds and a standard deviation of 0.25 pounds. Given this information, the probability of a sack weighing more than 2.40 pounds is 0.4251.

Question 15

The normal distribution is one of the most frequently used discrete probability distributions.

Question 16

The standard normal distribution has a mean of 0 and a standard deviation of 1.0.

Question 17

For a continuous distribution the total area under the curve is equal to 100.

Question 18

The number of defects manufactured by workers in a small engine plant is an example of a discrete random variable.

Question 19

If the mean, median and mode are all equal for a continuous random variable, then the random variable is normally distributed.

Question 20

The standard normal distribution table provides probabilities for the area between the z-value and the population mean.

Question 21

Service time for customers at a drive-through coffee shop has been shown to be uniformly distributed between 2 and 10 minutes. Customers will complain when service time exceeds 7.5 minutes. Based on this information, the probability of getting a complaint based on service time is 0.3125.

Question 22

An electronics repair shop has determined that the time between failures for a particular electronic component part is exponentially distributed with a mean time between failures of 200 hours. Based on this information, the probability that a part will fail between 20 and 100 hours is approximately 0.30.

Question 23

The Varden Packaging Company has a contract to fill 50-gallon barrels with gasoline for use by the U.S. Army. The machine that Varden uses has an adjustable device that allows the average fill per barrel to be adjusted as desired. However, the actual distribution of fill volume from the machine is known to be normally distributed with a standard deviation equal to 0.5 gallons. The contract that Varden has with the military calls for no more than 2 percent of all barrels to contain less than 49.2 gallons of gasoline. Suppose Varden managers are unwilling to set the mean fill at any level higher than 50 gallons. Given that, in order to meet the requirements, they will need to increase the standard deviation of fill volume.

Question 24

An assembly process takes between 20 and 40 minutes to complete with the distribution of time thought to be uniformly distributed. Based on this, the percentage of assemblies that require less than 25 minutes is 0.05.

Question 25

The Varden Packaging Company has a contract to fill 50 gallon barrels with gasoline for use by the U.S. Army. The machine that Varden uses has an adjustable device that allows the average fill per barrel to be adjusted as desired. However, the actual distribution of fill volume from the machine is known to be normally distributed with a standard deviation equal to 0.5 gallons. The contract that Varden has with the military calls for no more than 2 percent of all barrels to contain less than 49.2 gallons of gasoline. In order to meet this requirement, Varden should set the mean fill to approximately 49.92 gallons.

Question 26

Suppose the time it takes for a customer to be served at a fast-food chain business is thought to be uniformly distributed between 3 and 8 minutes, then the probability that it will take exactly 5 minutes is 0.20.

Question 27

A seafood shop sells salmon fillets where the weight of each fillet is normally distributed with a mean of 1.6 pounds and a standard deviation of 0.3 pounds. Based on this information we can conclude that 90 percent of the fillets weight more than 1.0 pound.

Question 28

If the time it takes for a customer to be served at a fast-food chain business is thought to be uniformly distributed between 3 and 8 minutes, then the probability that the time it takes for a randomly selected customer to be served will be less than 5 minutes is 0.40.

Question 29

Suppose the time it takes for a customer to be served at a fast-food chain business is thought to be uniformly distributed between 3 and 8 minutes, then the probability that a customer is served in less than 3 minutes is 0.

Question 30

It has been determined the weight of bricks made by the Dillenger Stone Company is uniformly distributed between 1 and 1.5 pounds. Based on this information, the probability that two randomly selected bricks will each weigh more than 1.3 pounds is 0.16.

Question 31

For a normal distribution, the probability of a value being between a positive z-value and its population mean is the same as that of a value being between a negative z-value and its population mean.

Question 32

One of the basic differences between a uniform probability distribution and a normal probability distribution is that the uniform is symmetrical but the normal is skewed depending on the value of the standard deviation.

Question 33

The miles per gallon for hybrid vehicles on city streets have been determined to be normally distributed with a mean of 33.2 mpg and a variance of 16. Based on this information, the probability that if three randomly selected vehicles are monitored and that two of the three will exceed the 35 mpg is slightly greater than 0.18.

Question 34

An electronics repair shop has determined that the time between failures for a particular electronic component part is exponentially distributed with a mean time between failures of 200 hours. Based on this information, the probability that a part will fail in the first 20 hours is approximately 0.095.

Question 35

The amount of drying time for the paint applied to a plastic component part is thought to be uniformly distributed between 30 and 60 minutes. Currently, the automated process selects the part from the drying bin after the part has been there for 50 minutes. Based on this, the probability that a part selected will not be dry is approximately 0.33.

Question 36

If a uniform distribution and normal distribution both have the same mean and the same range, the normal distribution will have a larger standard deviation than the uniform distribution

Question 37

A seafood shop sells salmon fillets where the weight of each fillet is normally distributed with a mean of 1.6 pounds and a standard deviation of 0.3 pounds. They want to classify the largest fillets as extra large and charge a higher price for them. If they want the largest 15 percent of the fillets to be classified as extra large, the minimum weight for an extra large fillet should be 1.91 pounds.

Question 38

Any normal distribution can be converted to a standard normal distribution.

Question 39

The Varden Packaging Company has a contract to fill 50-gallon barrels with gasoline for use by the U.S. Army. The machine that Varden uses has an adjustable device that allows the average fill per barrel to be adjusted as desired. However, the actual distribution of fill volume from the machine is known to be normally distributed with a standard deviation equal to 0.5 gallons. The contract that Varden has with the military calls for no more than 2 percent of all barrels to contain less than 49.2 gallons of gasoline. In order to meet this requirement, Varden should set the mean fill to approximately 50.225 gallons.

Question 40

The amount of drying time for the paint applied to a plastic component part is thought to be uniformly distributed between 30 and 60 minutes. Currently, the automated process selects the part from the drying bin after the part has been there for 50 minutes. The probability that none of three parts picked are still wet when they are selected is approximately 0.04.

Question 41

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. Based on this, what is the probability that a call will last longer than 13 minutes?

A) About 0.0125
B) Approximately 0.4875
C) About 0.5125
D) About 0.9875

Question 42

The manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a standard deviation equal to $80. Based on this information, what are the chances that the revenue on the first show will be between $300 and $500?

A) About 0.3062
B) Approximately 0.6534
C) 0.1736
D) Approximately 0.4798

Question 43

A study of cars arriving at a parking structure at the local airport shows that the time between arrivals is 1.2 minutes and is exponentially distributed. Based on this information, the mean number of cars arriving per minute is about 0.83.

Question 44

An electronics repair shop has determined that the time between failures for a particular electronic component part is exponentially distributed with a mean time between failures of 200 hours. Based on this information, the probability that a part will not fail in the first 200 hours is 0.50.

Question 45

Which of the following probability distributions could be used to describe the distribution for a continuous random variable?

A) Exponential distribution
B) Normal distribution
C) Uniform distribution
D) All of the above

Question 46

A major U.S. automaker has determined that the city mileage for one of its new SUV models is normally distributed with a mean equal to 15.2 mpg. A report issued by the company indicated that 22 percent of the SUV model vehicles will get more than 17 mpg in the city. Given this information, what is the city mileage standard deviation for this SUV model?

A) 0.77 mpg
B) Approximately 2.34 mpg
C) 1.8 mpg
D) Approximately 3.1 mpg

Question 47

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. The manager has decided to have a signal system attached to the phone so that after a certain period of time, a sound will occur on her employees' phone if she exceeds the time limit. The manager wants to set the time limit at a level such that it will sound on only 8 percent of all calls. The time limit should be:

A) 10.35 minutes.
B) approximately 5.19 minutes.
C) about 14.58 minutes.
D) about 11.23 minutes.

Question 48

Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $0.35 and a standard deviation of $0.33. Based on this information, what is the probability that a randomly selected stock will be lower by $0.40 or more?

A) 2.27
B) 0.4884
C) 0.0116
D) 0.9884

Question 49

Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 220 words per minute. If two students were selected at random, what is the probability that they would both read at less than 400 words per minute?

A) 0.4938
B) 0.0062
C) 0.00004
D) 0.2438

Question 50

The makers of Sweet-Things candy sell their candy by the box. Based on company policy, the mean target weight of all boxes is 2.0 pounds. To make sure that they are not putting too much in the boxes, the manager wants no more than 3 percent of all boxes to contain more than 2.10 pounds of candy. In order to do this, with a mean weight of 2 pounds, what must the standard deviation be? Assume that the box weights are normally distributed.

A) Approximately 0.05 pounds
B) -0.133 pounds
C) 1.144 pounds
D) None of the above

Question 51

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. What is the probability that three randomly monitored calls will each be completed in 4 minutes or less?

A) 0.4756
B) Approximately 0.1076
C) About 0.00001
D) Can't be determined without more information.

Question 52

Which of the following is not a characteristic of the normal distribution?

A) Symmetric
B) Mean = median = mode
C) Bell-shaped
D) Equal probabilities at all values of x

Question 53

The manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a variance equal to 1,456. Based on this information, what are the chances that the revenue on the first show will exceed $800?

A) 0.1255
B) Essentially zero
C) 0.3745
D) 0.9999

Question 54

A study of cars arriving at a parking structure at the local airport shows that the time between arrivals is 1.2 minutes and is exponentially distributed. The probability that more than 2 minutes will elapse between the arrivals of cars is about 0.81.

Question 55

A recent study showed that the length of time required for customers to resolve their computer issues with online support is normally distributed with a mean equal to 0.35 hours with a standard deviation of 0.2 hours. Given this information, what is the probability of resolution will take between 10 and 15 minutes?

A) About 0.13
B) Nearly 0.00
C) About 0.31
D) About 0.87

Question 56

Which of the following probability distributions can be used to describe the distribution for a continuous random variable?

A) Normal distribution
B) Binomial distribution
C) Poisson distribution
D) Hypergeometric

Question 57

Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 220 words per minute. Based on this information, what is the probability of a student reading at more than 1400 words per minute after finishing the course?

A) 0.0202
B) 0.5207
C) 0.4798
D) 0.9798

Question 58

Suppose that it is believed that investor returns on equity investments at a particular brokerage house are normally distributed with a mean of 9 percent and a standard deviation equal to 3.2 percent. What percent of investors at this brokerage house earned at least 5 percent?

A) 89.44 percent
B) 10.56 percent
C) 39.44 percent
D) 100 percent

Question 59

Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $.35 and a standard deviation of $.33. Based on this information, what is the probability that a randomly selected stock will close up $.75 or more?

A) 0.3869
B) 0.1131
C) 0.7100
D) 0.8869

Question 60

The makers of Sweet-Things candy sell their candy by the box. Based on company policy, the mean target weight of all boxes is 2.0 pounds. To make sure that they are not putting too much in the boxes, the manager wants no more than 3 percent of all boxes to contain more than 2.10 pounds of candy. In order to do this, what should the mean fill weight be set to if the fill standard deviation is 0.13 pounds? Assume that the box weights are normally distributed.

A) Just over 2 pounds
B) Approximately 2.33 pounds
C) Nearly 1.27 pounds
D) Approximately 1.86 pounds

Question 61

In a standard normal distribution, the probability P(-1.00< z < 1.20) is the same as:

A) P(1< z < 1.20) - P(0 < z < 1.00).
B) P(1< z < 1.20) - 2*P(0 < z < 1.00).
C) 2 ∗ P(1< z < 1.20) - P(0 < z <1.00).
D) P(1 < z < 1.20) + 2 ∗ P(0 < z <1.00).

Question 62

Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. The company has decided to give a cash payment to any employee that returns over a specified amount of sick leave minutes. Assuming that the company wishes no more than 5 percent of all employees to get a cash payment, what should the required number of minutes be?

A) 24 minutes
B) 419 minutes
C) 456 minutes
D) 470 minutes

Question 63

Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. The company has decided to give a cash payment to any employee that returns over 400 minutes of sick leave at the end of the year. What percentage of employees could expect a cash payment?

A) 16.67 percent
B) 0.1667 percent
C) Just over 43 percent
D) 80 percent

Question 64

It is assumed that the time customers spend in a record store is uniformly distributed between 3 and 12 minutes. Based on this information, what is the probability that a customer will spend more than 9 minutes in the record store?

A) 0.33
B) 0.1111
C) 0.67
D) 0.25

Question 65

A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes. The company is thinking of charging a lower rate for customers who use the phone less than a specified amount. If it wishes to give the rate reduction to no more than 12 percent of its customers, what should the cut-off be?

A) About 237 minutes
B) About 654 minutes
C) About 390 minutes
D) About 325 minutes

Question 66

The transportation manager for the State of New Jersey has determined that the time between arrivals at a toll booth on the state's turnpike is exponentially distributed with λ = 4 cars per minute. Based on this information, the standard deviation for the time between arrivals is:

A) 25 seconds.
B) 3.87 seconds.
C) 15 seconds.
D) 2 minutes.

Question 67

In a standard normal distribution, the probability that z is greater than 0 is:

A) 0.5
B) equal to 1
C) at least 0.5
D) 1.96

Question 68

It is thought that the time between customer arrivals at a fast food business is exponentially distributed with λ equal to 5 customers per hour. Given this information, what is the mean time between arrivals?

A) 12 minutes
B) 5 minutes
C) 5 hours
D) 2 minutes

Question 69

A store sells 6 different models of cell phones and have found that they sell an equal number of each model. The probability distribution that would describe this random variable is called:

A) uniform distribution.
B) Poisson distribution.
C) continuous distribution.
D) relative frequency distribution.

Question 70

A professor noted that the grades of his students were normally distributed with a mean of 75.07 and a standard deviation of 11.65. If only 10 percent of the students received grades of A, what is the minimum score needed to receive an A?

A) 80.00
B) 85.00
C) 90.00
D) 95.00

Question 71

It is assumed that the time customers spend in a record store is uniformly distributed between 3 and 12 minutes. Based on this information, what is the probability that a customer will be exactly 7.50 minutes in the record store?

A) 0.1250
B) 0.05
C) Essentially zero
D) 0.111

Question 72

A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes. As a promotion, the company plans to hold a drawing to give away one free vacation to Hawaii for a customer who uses between 400 and 402 minutes during a particular month. Based on the information provided, what proportion of the company's customers would be eligible for the drawing?

A) Approximately 0.1026
B) About 0.004
C) Approximately 0.2013
D) About 0.02

Question 73

The transportation manager for the State of New Jersey has determined that the time between arrivals at a toll booth on the state's turnpike is exponentially distributed with λ = 4 cars per minute. Based on this, the average time between arrivals is:

A) 15 seconds.
B) 12 seconds.
C) 25 seconds.
D) 4 minutes.

Question 74

Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. Based on this information, what is the probability that an employee will have less than 20 minutes of unused sick time?

A) 0.002
B) 0.966
C) 0.063
D) 0.042

Question 75

A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes. The company is thinking of changing its fee structure so that anyone who uses the phone less than 250 minutes during a given month will pay a reduced monthly fee. Based on the available information, what percentage of current customers would be eligible for the reduced fee?

A) About 36.4 percent
B) Approximately 52 percent
C) About 86.6 percent
D) About 13.6 percent

Question 76

It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. What is the probability that a component will be functioning after 60 hours?

A) Approximately 0.30
B) About 0.70
C) About 0.21
D) About 0.49

Question 77

Which of the following probability distributions would most likely be used to describe the time between failures for electronic components?

A) Binomial distribution
B) Exponential distribution
C) Uniform distribution
D) Normal distribution

Question 78

Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. Based on this information, what is the probability that three randomly chosen employees have over 400 unused sick minutes at the end of the year?

A) 0.1667
B) 0.0046
C) 0.5001
D) 0.0300

Question 79

It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. If one extra component is installed as a backup, what is the probability of at least one of the two components working for at least 60 hours?

A) About 0.51
B) About 0.09
C) About 0.06
D) About 0.70

Question 80

It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. Based on this information, what is the probability that a randomly selected part will fail in less than 10 hours?

A) About 0.82
B) About 0.20
C) About 0.33
D) About 0.18