Deck 6: Continuous Random Variables and the Normal Distribution

Question 1

For a normal distribution,the z value for an x value that is to the right of the mean is always:

A)equal to zero
B)negative
C)greater than 1
D)positive

Answer 1

positive

Question 2

The probability that a continuous random variable x assumes a single value is always:

A)less than 1
B)greater than zero
C)equal to zero
D)between zero and 1

Answer 2

equal to zero

Question 3

A continuous random variable is a random variable that can:

A)assume only a countable set of values
B)assume any value in one or more intervals
C)have no random sample
D)assume no continuous random frequency

Answer 3

assume any value in one or more intervals

Question 4

The relative frequency density for a class is obtained by dividing the:

A)frequency of that class by the class width
B)relative frequency of that class by the total frequency
C)relative frequency of that class by the class width
D)frequency of that class by the relative frequency

Question 5

For a continuous random variable x,the area under the probability distribution curve between any two points is always:

A)greater than 1
B)less than zero
C)equal to 1
D)in the range zero to 1

Question 6

For the standard normal distribution,the mean is:

A)1 and the standard deviation is zero
B)0.5 and the standard deviation is 0.5
C)zero and the standard deviation is 1
D)1 and the standard deviation is 1

Question 7

The total area under a normal distribution curve to the right of the mean is always:

A)equal to 1
B)equal to zero
C)equal to 0.5
D)greater than .5

Question 8

For a normal distribution,the z value for the mean is always:

A)equal to zero
B)negative
C)equal to 1
D)positive

Question 9

For the standard normal distribution,the z value gives the distance between the mean and a point in terms of the:

A)mean
B)standard deviation
C)variance
D)center of the curve

Question 10

For a continuous random variable x,the probability that x assumes a value in an interval is:

A)in the range zero to 1
B)greater than 1
C)less than zero
D)greater than 2

Question 11

The parameters of the normal distribution are:

A)
B)
C)
D)

Question 12

The total area under a normal distribution curve to the left of the mean is always:

A)equal to 1
B)equal to zero
C)equal to 0.5
D)greater than .5

Question 13

For a continuous random variable x,the total probability of all (mutually exclusive)intervals within which x can assume a value is:

A)less than 1
B)greater than 1
C)equal to 1
D)between zero and 1

Question 14

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

A)The total area under the curve is 1.0
B)The curve is symmetric about the mean
C)The value of the mean is always greater than the value of the standard deviation
D)The two tails of the curve extend indefinitely

Question 15

The tails of a normal distribution curve:

A)meet the horizontal axis at z = 3.0
B)never meet or cross the horizontal axis
C)cross the horizontal axis at z = 4.0
D)are nonsymmetric

Question 16

For a continuous random variable x,the total area under the probability distribution curve of x is always:

A)less than 1
B)greater than 1
C)equal to 1
D)between zero and 1

Question 17

For the standard normal distribution,the area between z = 0 and z = 1.70,rounded to four decimal places,is:

Question 18

For a normal distribution,the spread of the curve decreases and its height increases as:

A)the sample size decreases
B)the standard deviation decreases
C)the ratio of the mean and standard deviation increases
D)the mean increases

Question 19

The normal probability distribution is applied to:

A)a discrete random variable
B)a continuous random variable
C)any random variable
D)a subjective random variable

Question 20

For a normal distribution,the z value for an x value that is to the left of the mean is always:

A)equal to zero
B)negative
C)less than 1
D)positive

Question 21

For the standard normal distribution,the area between z = -2.35 and z = -1.56,rounded to four decimal places,is:

Question 22

Use the following to answer questions :
The GMAT scores of all examinees who took that test this year produce a distribution that is approximately normal with a mean of 420 and a standard deviation of 32.
The probability that the score of a randomly selected examinee is more than 530,rounded to four decimal places,is:

Question 23

Use the following to answer questions :
The GMAT scores of all examinees who took that test this year produce a distribution that is approximately normal with a mean of 420 and a standard deviation of 32.
The probability that the score of a randomly selected examinee is less than 370,rounded to four decimal places,is:

Question 24

For the standard normal distribution,the area to the left of z = -2.22,rounded to four decimal places,is:

Question 25

Use the following to answer questions :
The GMAT scores of all examinees who took that test this year produce a distribution that is approximately normal with a mean of 420 and a standard deviation of 32.
The probability that the score of a randomly selected examinee is between 400 and 480,rounded to four decimal places,is:

Question 26

For the standard normal distribution,the area between z = 1.03 and z = 1.30,rounded to four decimal places,is:

Question 27

For the standard normal distribution,the area to the left of z = 1.23,rounded to four decimal places,is:

Question 28

For the standard normal distribution,the area to the right of z = 0.53,rounded to four decimal places,is:

Question 29

For the standard normal distribution,the area to the right of z = -2.97,rounded to four decimal places,is:

Question 30

Let x have a normal distribution with a mean of 7.8 and a standard deviation of 3.58.The z value for x = 10.27,rounded to two decimal places,is:

Question 31

For the standard normal distribution,the area between z = -2.04 and z = 2.28,rounded to four decimal places,is:

Question 32

Use the following to answer questions :
The daily sales at a convenience store produce a distribution that is approximately normal with a mean of 1220 and a standard deviation of 130.
The probability that the sales on a given day at this store are less than $1,305,rounded to four decimal places,is:

Question 33

Use the following to answer questions :
The daily sales at a convenience store produce a distribution that is approximately normal with a mean of 1220 and a standard deviation of 130.
The probability that the sales on a given day at this store are between $1,200 and $1,300,rounded to four decimal places,is:

Question 34

Use the following to answer questions :
The net weights of all boxes of Top Taste cookies produce a distribution that is approximately normal with a mean of 31.74 and a standard deviation of 0.58.
The probability that the net weight of a randomly selected box of these cookies is less than 31.58 ounces,rounded to four decimal places,is:

Question 35

For the standard normal distribution,the area between z = 0 and z = -1.38,rounded to four decimal places,is:

Question 36

Let x have a normal distribution with a mean of 123.7 and a standard deviation of 6.01.The z value for x = 133.67,rounded to two decimal places,is:

Question 37

Let x have a normal distribution with a mean of 49.2 and a standard deviation of 4.90.The z value for x = 56.05,rounded to two decimal places,is:

Question 38

Use the following to answer questions :
The daily sales at a convenience store produce a distribution that is approximately normal with a mean of 1220 and a standard deviation of 130.
The probability that the sales on a given day at this store are more than $1,405,rounded to four decimal places,is:

Question 39

Use the following to answer questions :
The net weights of all boxes of Top Taste cookies produce a distribution that is approximately normal with a mean of 31.74 and a standard deviation of 0.58.
The probability that the net weight of a randomly selected box of these cookies is more than 32.6 ounces,rounded to four decimal places,is:

Question 40

Let x have a normal distribution with a mean of -40.3 and a standard deviation of 11.51.The z value for x = -26.58,rounded to two decimal places,is:

Question 41

There are 250 players in a particular youth soccer league that has 11 teams.The league statistician is tabulating the total goals scored over the past season by each player.She assigns the random variable y to represent these totals,and then assigns the following categories for y: 0 to less than 4,4 to less than 8,8 to less than 12,12 to less than 16,16 to less than 20,and 20 to less than 24.The relative frequency density for the 8 to less than 12 class is 0.019.How many of the players scored between 8 and less than 12 goals?

Question 42

Use the following to answer questions :
The net weights of all boxes of Top Taste cookies produce a distribution that is approximately normal with a mean of 31.74 and a standard deviation of 0.58.
The probability that the net weight of a randomly selected box of these cookies is between 31.8 and 32.5 ounces,rounded to four decimal places,is:

Question 43

Use the following to answer questions :
In a recent Gallup poll,52% of parents with children under 18 years of age gave themselves a grade of B for the job they are doing bringing up their kids.Assume that this percentage is true for the current population of all parents with children under 18 years of age.You take a random sample of 1044 such parents and ask them to give themselves a grade for the job they are doing bringing up their kids.
The probability that 550 or less will give themselves a grade of B is approximately: (Round the answer to 4 decimal places.)

Question 44

Use the following to answer questions :
We know that football is the favorite sport to watch on television for 36% of adults in the United States.Suppose we take a random sample of 522 adults and obtain their opinions on their favorite sport to watch on television.
The probability that 180 to 215 will say that football is their favorite sport to watch on television is approximately: (Round the answer to 4 decimal places.)

Question 45

Use the following to answer questions :
The heights of all female college basketball players produce a distribution that is approximately normal with a mean of 67.55 and a standard deviation of 2.02.
The probability that the height of a randomly selected female college basketball player is between 63.9 and 69.2 inches,rounded to four decimal places,is:

Question 46

The area under the standard normal curve from zero to z is 0.1772 and z is negative.The value of z is:

Question 47

The area under the standard normal curve to the left of z is 0.0401 and z is negative.The value of z is:

Question 48

Use the following to answer questions :
The heights of all female college basketball players produce a distribution that is approximately normal with a mean of 67.55 and a standard deviation of 2.02.
The probability that the height of a randomly selected female college basketball player is less than 67.2 inches,rounded to four decimal places,is:

Question 49

The area under the standard normal curve to the right of z is 0.0089 and z is positive.The value of z is:

Question 50

Use the following to answer questions :
We know that 57% of all adults are in favor of abolishing the sales tax and increasing the income tax.Suppose we take a random sample of 420 adults and obtain their opinions on the issue.
The probability that 250 to 265 will be in favor of abolishing the sales tax and increasing the income tax is approximately:

Question 51

Use the following to answer questions :
We know that 57% of all adults are in favor of abolishing the sales tax and increasing the income tax.Suppose we take a random sample of 420 adults and obtain their opinions on the issue.
The probability that exactly 250 will be in favor of abolishing the sales tax and increasing the income tax is approximately:

Question 52

Use the following to answer questions :
We know that football is the favorite sport to watch on television for 36% of adults in the United States.Suppose we take a random sample of 522 adults and obtain their opinions on their favorite sport to watch on television.
The probability that 193 or more will say that football is their favorite sport to watch on television is approximately: (Round the answer to 4 decimal places.)

Question 53

Use the following to answer questions :
The heights of all female college basketball players produce a distribution that is approximately normal with a mean of 67.55 and a standard deviation of 2.02.
The probability that the height of a randomly selected female college basketball player is more than 65.8 inches,rounded to four decimal places,is:

Question 54

Use the following to answer questions :
In a recent Gallup poll,52% of parents with children under 18 years of age gave themselves a grade of B for the job they are doing bringing up their kids.Assume that this percentage is true for the current population of all parents with children under 18 years of age.You take a random sample of 1044 such parents and ask them to give themselves a grade for the job they are doing bringing up their kids.
The probability that 560 or more will give themselves a grade of B is approximately: (Round the answer to 4 decimal places.)

Question 55

We can use the normal distribution to approximate the binomial distribution when:

A)the sample size is at least 30
B)np and nq are both less than 5
C)np and nq are both more than 5
D)nx is greater than 30

Question 56

Use the following to answer questions :
In a recent Gallup poll,52% of parents with children under 18 years of age gave themselves a grade of B for the job they are doing bringing up their kids.Assume that this percentage is true for the current population of all parents with children under 18 years of age.You take a random sample of 1044 such parents and ask them to give themselves a grade for the job they are doing bringing up their kids.
The probability that 520 to 555 will give themselves a grade of B is approximately: (Round the answer to 4 decimal places.)

Question 57

The area under the standard normal curve from zero to z is 0.4906 and z is positive.The value of z is:

Question 58

Use the following to answer questions :
We know that football is the favorite sport to watch on television for 36% of adults in the United States.Suppose we take a random sample of 522 adults and obtain their opinions on their favorite sport to watch on television.
The probability that 170 to 190 will say that football is their favorite sport to watch on television is approximately: (Round the answer to 4 decimal places.)

Question 59

Use the following to answer questions :
We know that 57% of all adults are in favor of abolishing the sales tax and increasing the income tax.Suppose we take a random sample of 420 adults and obtain their opinions on the issue.
The probability that 225 or fewer will be in favor of abolishing the sales tax and increasing the income tax is approximately:

Question 60

The accountant at a department store is analyzing the credit card purchases of 100 of the store's cardholders over the past year.The following table lists the frequency distribution of the continuous random variable x,annual credit card purchases.
What is the relative frequency density of the 400 to less than 600 class? Round your answer to 5 decimal places.

Question 61

Let x be a continuous random variable that follows a normal distribution with a mean of 218 and a standard deviation of 26.
Find the value of x so that the area under the normal curve to the left of x is approximately 0.8770.Round your answer to two decimal places.

Question 62

Let x be a continuous random variable that follows a normal distribution with a mean of 226 and a standard deviation of 31.
Find the value of x so that the area under the normal curve between and x is approximately 0.4959 and the value of x is less than .Round your answer to two decimal places.

Question 63

For a normal curve,changing the mean from 35 to 46 will cause the curve to shift

A)to the left.
B)to the right.
C)up.
D)down.

Question 64

Suppose that the random variable x has a binomial distribution with n = 30 and p = 0.48.You want to determine .Using the normal approximation,what is this probability? (Round the answer to 4 decimal places.)

Question 65

According to the Empirical rule,68.26% of the data would fall between what two values for a population with mean of 816 and standard deviation of 248?

Question 66

The ages of adults in a certain community follow a normal distribution with mean 38.5 and standard deviation 6.68.The random variable x represents the age of a randomly selected adult from this community.Given that ,what is a to the nearest year?

Question 67

Let x be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation of 51.
Find the value of x so that the area under the normal curve to the right of x is approximately 0.2946.Round your answer to two decimal places.

Question 68

Suppose that the distribution for a random variable x is normal with mean 15 and standard deviation ,and .Rounded to two decimal places,what is ?

Question 69

Let x be a continuous random variable that follows a normal distribution with a mean of 207 and a standard deviation of 42.
Find the value of x so that the area under the normal curve between and x is approximately 0.4996 and the value of x is greater than .Round your answer to two decimal places.

Question 70

A floor tiling contractor has just sent Tina out on a job without any indication of the size of the job.She does know that,over the years,the number of tiles required for each job has followed a normal distribution with a mean of 581 and a standard deviation of 210.She can either take the large truck (which is very difficult and expensive to drive)or the small truck to the job site.She is certain that the large truck can hold enough tiles to do the job,but she would prefer to take the small truck if she can.The small truck can carry up to 750 tiles.Because the job site is out of town,she can only make one trip.What is the probability that the small truck will carry enough tiles to do the job?

Question 71

According to the Empirical rule,what percent of the data should be between 136 and 260 for a population with mean of 198 and standard deviation of 62?

Question 72

As explained in the textbook,the normal distribution can be used as an approximation to the binomial distribution when np > 5 and nq > 5.Let x be the number of times that heads comes up in n flips of a coin for which the probability of a head is p = 0.152.What is the lowest that n can be in order for us to use the normal approximation for the distribution of x?

Question 73

You are given that the area under the standard normal curve to the left of z = -2.56 is equal to 0.0052.What is P(-2.56< z < 2.56)?

Question 74

We know that the length of time required for a student to complete a particular aptitude test has a normal distribution with a mean of 41.5 minutes and a variance of 3.1 minutes.What is the probability,rounded to four decimal places,that a given student will complete the test in more than 36 minutes but less than 44 minutes?