Question 1

It is appropriate to use the uniform distribution to describe a continuous random variable x when:

Accepted Answer

A)  The area under the probability curve = 1.
B)  The probability curve f(x) > 0.
C)  The shape of the histogram of all possible values of x is nonsymmetrical.
D)  Relative frequencies of all possible values of x are about the same. D

Question 2

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?

Accepted Answer

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

Question 3

During the past six months,73.2 percent of US households purchased sugar.Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10.What proportion of the households spent between $5.00 and $9.00 on sugar?

Accepted Answer

A)  .7611
B)  .7628
C)  .0017
D)  .7594 D

Question 4

The weight of a product is normally distributed with a standard deviation of .5 ounces.What should the average weight be if the production manager wants no more than 10 percent of the products to weigh more than 4.8 ounces?

Accepted Answer

A)  3.52
B)  3.64
C)  5.44
D)  4.16

Question 5

While conducting experiments,a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?

Accepted Answer

A)  .79
B)  .45
C)  .55
D)  .50

Question 6

At an oceanside nuclear power plant,seawater is used as part of the cooling system.This raises the temperature of the water that is discharged back into the ocean.The amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° C.What is the probability that the temperature increase will be between 20° and 22° C?

Accepted Answer

A)  0.08
B)  0.88
C)  0.13
D)  0) 20

Question 7

The US local airport keeps track of the percentage of flights arriving within 15 minutes of their scheduled arrivals.The stem-and-leaf plot of the data for one year is below.
$\begin{array} { l l } 
76 & 9 \
77 & 114 \
78 & \
79 & 07 \
80 & 88 \
81 & 2 \
82 & 1 \
83 & 88
\end{array}$ 
Construct a normal probability plot and interpret the plot.

Accepted Answer

The answer of The US local airport keeps track of...

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

In order to approximate the binomial distribution using the normal distribution,the following condition(s)must be met if p is near 1.

Accepted Answer

A)  np > 5 only
B)  n must be larger than just meeting the condition of np > 5
C)  n can be as small as np > 5
D)  n > 5

Question 10

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.

Accepted Answer

A) True 
 B)False

Question 11

The weight of a product is normally distributed with a mean of four ounces and a variance of .25 "squared ounces." What is the probability that a randomly selected unit from a recently manufactured batch weighs no more than 3.5 ounces?

Accepted Answer

A)  .8413
B)  .9772
C)  .1587
D)  .0228

Question 12

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.

Accepted Answer

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

Question 13

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?

Accepted Answer

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

Question 14

Which of the following is a continuous distribution?

Accepted Answer

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

Question 15

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.

Accepted Answer

A) True 
 B)False

Question 16

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:

Accepted Answer

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 17

____________ 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.

Accepted Answer

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

Question 18

The mean life of a 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?

Accepted Answer

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

Question 19

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state.The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.What is the probability that a randomly selected apple will contain more than 2.50 ounces?

Accepted Answer

A)  .9525
B)  .4525
C)  .0475
D)  .5474

Question 20

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes.Complete the following statement: Only 20 percent of the individuals wait less than _____ minutes.

Accepted Answer

A)  36.72
B)  23.28
C)  34.63
D)  25.37

Exam 6: Continuous Random Variables

It is appropriate to use the uniform distribution to describe a continuous random variable x when:

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?

During the past six months,73.2 percent of US households purchased sugar.Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10.What proportion of the households spent between $5.00 and $9.00 on sugar?

The weight of a product is normally distributed with a standard deviation of .5 ounces.What should the average weight be if the production manager wants no more than 10 percent of the products to weigh more than 4.8 ounces?

While conducting experiments,a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?

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

In order to approximate the binomial distribution using the normal distribution,the following condition(s) must be met if p is near 1.

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.

The weight of a product is normally distributed with a mean of four ounces and a variance of .25 "squared ounces." What is the probability that a randomly selected unit from a recently manufactured batch weighs no more than 3.5 ounces?

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.

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?

Which of the following is a continuous distribution?

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.

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:

____________ 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.

The mean life of a 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?