Deck 6: Continuous Random Variables

Question 1

The exponential probability distribution is based on a continuous random variable.

Answer 1

True

Question 2

The mean and median are the same for an exponential distribution.

Answer 2

False

Question 3

The z value tells us the number of standard deviations that a value x is from the mean.

Answer 3

True

Question 4

The mean life of pair of shoes is 40 months with a standard deviation of 8 months.If the life of the shoes is normally distributed,how many pairs of shoes out of one million will need replacement before 36 months?

A)500,000
B)808,500
C)191,500
D)308,500

Question 5

The mean of a standard normal distribution is always equal to 1.

Question 6

For a continuous distribution,the exact probability of a particular value is zero.

Question 7

A uniform distribution f(x)is a continuous probability distribution which says the probability that x is in any 2 intervals of equal length is the same.

Question 8

For a continuous distribution,P(X $\le$ 100)= P(X < 100).

Question 9

The standard deviation of a standard normal distribution is always equal to 1.

Question 10

The actual weight of hamburger patties is an example of a continuous random variable.

Question 11

The normal probability distribution is a discrete probability distribution.

Question 12

For a binomial probability experiment,with n = 150 and p = .2,it is appropriate to use the normal approximation to the binomial distribution.

Question 13

A continuous probability distribution having a rectangular shape where the probability is evenly distributed over an interval of numbers is called a uniform probability distribution.

Question 14

The number of defective pencils in a lot of 1000 is an example of a continuous random variable.

Question 15

If the random variable of x is normally distributed,68.26% of all possible observed values of x will be within two standard deviations of the mean.

Question 16

The height of a probability curve f(x)at a particular point indicates the value of a probability for a given value of a random variable x.

Question 17

The mean and median are the same for a normal distribution.

Question 18

In a statistical study,the random variable X = 1,if the house is colonial,and X = 0 if the house is not colonial,then it can be stated that the random variable is continuous.

Question 19

A continuous random variable may assume only integer values in a given interval.

Question 20

All continuous random variables are normally distributed.

Question 21

The MPG (Miles per Gallon)for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8.What is the probability that the MPG for a selected mid-size car would be: Less than 33.2?

A)43.32%
B)6.68%
C)93.32%
D)86.64%
E)13.36%

Question 22

The MPG (Miles per Gallon)for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8.What is the probability that the MPG for a selected mid-size car would be: More than 33.2?

A)43.32%
B)6.68%
C)93.32%
D)86.64%
E)13.36%

Question 23

The normal approximation of the binomial distribution is appropriate when:

A)np $\ge$ 5
B)n(1 - p) $\ge$ 5
C)np $\le$ 5
D)n(1 - p) $\le$ .5 and np $\le$ 5
E)np $\ge$ .5 and n(1 - p) $\ge$ 5

Question 24

If the random variable of x is normally distributed,____% of all possible observed values of x will be within three standard deviations of the mean.

A)68.26
B)95.44
C)99.73
D)100
E)None of the above

Question 25

The relationship between the standard normal random variable Z and normal random variable X is that:

A)Only the normal random variable X is continuous.
B)Only the standard normal variable Z is continuous.
C)The standard normal variable Z counts the number of standard deviations that the value of the normal random variable X is away from its mean.
D)The values of the standard normal random variable Z cannot be negative.
E)The values of the normal random variable X cannot be negative.

Question 26

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population,what is the probability that it will weigh less than 900 grams?

A)4772
B).9772
C).9544
D).0228
E).0456

Question 27

Which of the following statements is not a property of the normal probability distribution?

A)The normal distribution is symmetric.
B)95.44% of all possible observed values of the random variable x are within plus or minus three standard deviations of the population mean.
C)The mean,median,and mode are equal.
D)The area under the normal curve to the right of the mean is equal to the area under the normal curve to the left of the mean.
E)All of the above answers are properties of the normal distribution.

Question 28

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population,what is the probability that it will weigh more than 904 grams?

A).8849
B).3849
C).1151
D).7698
E).2302

Question 29

The _____________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.

A)Normal
B)Exponential
C)Poisson
D)Binomial
E)Uniform

Question 30

A standard normal distribution has a mean of _____ and standard deviation of _____.

A)zero,zero
B)zero,one
C)one,one
D)one,zero

Question 31

If the random variable X has a mean of µ and a standard deviation $\sigma$ then (X - µ)/ $\sigma$ has a mean and standard deviation respectively:

A)
B)
C)1 and 0
D)0 and 1

Question 32

A study shows that employees that begin their work day at 9:00 a.m.vary their times of arrival uniformly from 8:40 a.m.to 9:30 a.m.The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is:

A)40%
B)20%
C)10%
D)30%
E)16.7%

Question 33

The price-to-earning ratio for firms in a given industry is distributed according to normal distribution.In this industry,a firm with a standard normal variable value of Z = 1:

A)Has an above average price-to-earning ratio.
B)Has a below average price-to-earnings ratio.
C)Has an average price-to-earnings ratio.
D)May have an above average or below average price-to-earnings ratio.

Question 34

Which of the following is a continuous distribution?

A)Poisson
B)Hypergeometric
C)Exponential
D)Binomial

Question 35

If the wages of workers for a given company are normally distributed with a mean of $15 per hour,then the proportion of the workers earning more than $13 per hour:

A)Is greater than the proportion earning less than $13 per hour.
B)Is greater than the proportion earning less than $18 per hour.
C)Is less than 50%.
D)Is less than the proportion earning more than the mean wage.

Question 36

The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.

A)Less than
B)Greater than
C)Equal to
D)A,B,or C above dependent on the value of the mean
E)A,B,or C above dependent on the value of the standard deviation

Question 37

Values of the standard normal random variable are measured

A)With reference to specific units
B)In the units in which the mean is measured
C)In the number of standard deviations from the mean
D)In squared units in which the mean is measured
E)None of the above

Question 38

A property of continuous distributions is that:

A)As with discrete random variables,the probability distribution can be approximated by a smooth curve.
B)Probabilities for continuous variables can be approximated using discrete random variables.
C)Unlike discrete random variables,probabilities can be found using tables.
D)Unlike discrete random variables,the probability that a continuous random variable equals a specific value is zero [P(X = x)= 0].

Question 39

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams.We calculated the value of z for a specific box of this brand of cereal and the z value was negative.This negative z value indicates that:

A)We made a mistake in our calculations,as z must always be a nonnegative number.
B)The fill weight exceeds 910 grams.
C)The fill weight is less than 910 grams.
D)The fill weight is equal to 910 grams.
E)The fill weight may be more or less than 910 grams depending on the value of the standard deviation.

Question 40

A student's grade on an examination was transformed to a z value which is negative.Therefore,we know that he scored:

A)Higher than 16% of the class
B)Higher than 45% of the class
C)Above the first quartile
D)Below the mean
E)Lower than 16% of the class

Question 41

The z-value tells us the number of _____ that a value of x is from the mean.

A)Variances
B)Standard Deviations
C)Medians
D)Standard Means

Question 42

The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes.What is the probability that the service time: Is between 2 and 4 minutes?

A).2488
B).4493
C).2019
D).2474
E).1170

Question 43

The mean of a standard normal distribution is always equal to _______.

A)1
B)0.5
C)0
D)-1

Question 44

For a normal population with a mean of 10 and a variance 4,the P(X $\ge$ 10)is ___.

A)1.0
B)0.5
C)0.75
D)0.25

Question 45

_____________ values of the standard deviation results in a normal curve that is narrower and more peaked.

A)Smaller
B)Equal
C)Larger
D)Uniform

Question 46

__________ values of the standard deviation results in a normal curve that is wider and flatter.

A)Smaller
B)Equal
C)Larger
D)Uniform

Question 47

The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes.What is the probability that the service time: Exceeds 3 minutes?

A).3012
B).6988
C).4346
D).5654
E).0821

Question 48

When a ____________ probability distribution is used to approximate a ________ probability distribution we must make ____________ correction.

A)Continuous,discrete,continuity
B)Discrete,continuous,continuity
C)Continuous,discrete,finite population
D)None of the above

Question 49

The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes.What is the probability that the service time: Is no more than 3 minutes?

A).3012
B).6988
C).4346
D).5654
E).0821

Question 50

A probability distribution that describes the time or space between successive occurrences of an event is a(n)_____ probability distribution.

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

Question 51

Given that X is a normal random variable,the probability that a given value of X is below its mean is ________________.

A)1
B)equal to 0.5
C)less than 0.5
D)greater than 0.5

Question 52

The standard deviation of a standard normal distribution is always equal to _____.

A)1
B)0.5
C)0
D)-1

Question 53

The thickness of randomly selected metal piece is a ___________ random variable.

A)Poisson
B)Continuous
C)Discrete
D)Binomial

Question 54

The area under the curve of a valid continuous probability distribution must _____.

A)Equal 1
B)Be between 0 and 1
C)Be infinite
D)Be less than 1

Question 55

The specific shape of each normal distribution is determined by its _____ and _____.

A)Mean,Standard Deviation
B)Median,Standard Deviation
C)Mean,Variance
D)Median,Variance

Question 56

A continuous probability distribution that is useful in describing the time or space between successive occurrences of an event is a(n):

A)Uniform probability distribution
B)Normal probability distribution
C)Poisson probability distribution
D)Exponential probability distribution

Question 57

_____ theory is a methodology that attempts to determine the number of servers that strikes an optimum balance between the time customers wait for service and the cost of providing service.

A)Exponential
B)Binomial
C)Uniform Distribution
D)Queueing

Question 58

A continuous probability distribution having a rectangular shape where the probability is evenly distributed over an interval of numbers is a(n)_____ distribution.

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

Question 59

A normal distribution with mean zero and a standard deviation one is called the _____ normal distribution.

A)Continuous
B)Uniform
C)Exponential
D)Standard

Question 60

The number of standard deviations that a value x is from the mean is a(n)_____.

A)Variance
B)Exponential value
C)Z-score
D)Area

Question 61

An aptitude test has a mean score of 80 and a standard deviation of 5.The population of scores is normally distributed.What raw score corresponds to the 70^th percentile?

A)77.4
B)83.5
C)82.6
D)76.5

Question 62

The lifetime of a stereo component is exponentially distributed with mean 1,000 days.What is the probability that the lifetime: Exceeds 1,000 days?

A).6321
B).5000
C).3679
D)1.000

Question 63

An aptitude test has a mean score of 80 and a standard deviation of 5.The population of scores is normally distributed.What proportion of tests has scores over 90?

A).9772
B).0228
C).9544
D).0456

Question 64

The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours.What is the probability that the drone will fly: Between 4.70 and 4.82 hours?

A).1336
B).8664
C).9332
D).4332

Question 65

The time of travel from a person's apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes.If he/she leaves home at 9:05 AM,what is the probability that he/she will get to the station between 9:25 and 9:30 AM?

A)1.0
B)0
C)0.5
D)0.25

Question 66

The probability that an appliance is in repair is .5.If an apartment complex has 100 such appliances,what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial.

A).5000
B).0287
C).6000
D).9713

Question 67

What is the probability that a random variable having a standard normal distribution is between .87 and 1.28?

A).0919
B).4100
C).6517
D).3483

Question 68

If x is a binomial random variable where n = 100 and p = .1,find the probability that x is less than or equal to 10 using the normal approximation to the binomial.

A).9544
B).0446
C).5675
D).4325

Question 69

If the random variable of x is normally distributed,____ % of all possible observed values of x will be within two standard deviations of the mean.

A)99.73
B)68.26
C)95.00
D)95.44

Question 70

What is the probability that a standard normal random variable will be between .3 and 3.2?

A).6179
B).3808
C).6192
D).9987

Question 71

The lifetime of a stereo component is exponentially distributed with mean 1,000 days.What is the probability that the lifetime: Is greater than or equal to 700 days?

A).7603
B).5034
C).2397
D).4966

Question 72

Given the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet,what is the probability he throws it: Between 50 feet and 60 feet?

A).9972
B).5000
C).9544
D).4772

Question 73

Given the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet,what is the probability he throws it: No less than 55 feet?

A).8413
B).1587
C).6826
D).3174

Question 74

The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours.What is the probability that the drone will fly: Less than 4.66 hours?

A)-.0062
B).5062
C).0062
D).9938

Question 75

The life of a light bulb is exponentially distributed with a mean of 1,000 hours.What is the probability that the bulb will last: More than 1,200 hours?

A).3012
B).3679
C).4345
D).6988

Question 76

The time between breakdowns of an alarm system is exponentially distributed with mean 10 days.What is the probability that there are no breakdowns on a given day?

A).9048
B).3679
C).0952
D)0.000

Question 77

The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours.What is the probability that the drone will fly: More than 4.80 hours?

A).1587
B).8413
C).6587
D)/3413

Question 78

The life of a light bulb is exponentially distributed with a mean of 1,000 hours.What is the probability that the bulb will last: Less than 800 hours?

A).6321
B).5507
C).7135
D).4493

Question 79

If the scores on an aptitude test are normally distributed with mean 500 and standard deviation 100,what proportion of the test scores are less than 585?

A).1977
B).8500
C).1500
D).8023

Question 80

What is the probability that a standard normal random variable will be between -2 and 2?

A).4772
B).0228
C).9772
D).9544