Deck 7: Normal Curves and Sampling Distributions

Question 1

Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean $\mu$ = 21.1 kilograms and standard deviation $\sigma$ = 3.7 kilograms. Let x be the weight of a fawn in kilograms. Convert the following z interval to a x interval. $$- 3.1 < z$$

A)x < -9.63
B)x < 9.63
C)x > 9.63
D)x > 32.57
E)x > -32.57

Answer 1

x > 9.63

Question 2

At a certain excavation site, archaeological studies have used the method of tree-ring dating in an effort to determine when people lived in there. Wood from several excavations gave a mean of (year) 899 with a standard deviation of 38 years. The distribution of dates was more or less mound-shaped and symmetrical about the mean. Use the empirical rule to estimate a range of years centered about the mean in which about 68.3% of the data (tree-ring dates) will be found.

A)from 975 to 1013
B)from 861 to 1013
C)from 899 to 1013
D)from 785 to 861
E)from 861 to 937

Answer 2

from 861 to 937

Question 3

Find the area under the standard normal curve over the interval specified below. To the right of z =2

A)0.159
B)0.500
C)0.841
D)0.999
E)0.023

Answer 3

0.023

Question 4

Find the area under the standard normal curve over the interval specified below. To the left of z = 0

A)0.999
B)0.500
C)0.023
D)0.977
E)0.159

Question 5

Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean $\mu$ = 22.4 kilograms and standard deviation $\sigma$ = 4.9 kilograms. Let x be the weight of a fawn in kilograms. Convert the following x interval to a z interval. Round to the nearest hundredth. $$x < 36.1$$

A)z > -2.80
B)z < 2.80
C)z < 11.94
D)z < -2.80
E)z > 2.80

Question 6

Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose for healthy females, x has an approximately normal distribution with mean $\mu$ = 4.9 and standard deviation $\sigma$ =0.5 Convert the following x interval from a laboratory test to a z interval. 6.9 < x

A)1 > z
B)4 > z
C)4 < z
D)-4 > z
E)-1 > z

Question 7

Let z be a random variable with a standard normal distribution. Find the indicated probability below. P(z $\le$ -1.6)

A)0.945
B)0.055
C)0.027
D)0.973
E)0.018

Question 8

Let z be a random variable with a standard normal distribution. Find the indicated probability below. P(z $\ge$ -0.9)

A)0.816
B)0.092
C)0.158
D)0.184
E)0.316

Question 9

Let z be a random variable with a standard normal distribution. Find the indicated probability below. P(-1.7 $\le$ z $\le$ -0.8)

A)0.816
B)0.167
C)0.212
D)0.788
E)0.955

Question 10

Assuming that the heights of college women are normally distributed with mean 67 inches and standard deviation 3 inches, what percentage of women are taller than 58 inches?

A)0.1%
B)99.9%
C)2.3%
D)84.1%
E)15.9%

Question 11

Assuming that the heights of college women are normally distributed with mean 63 inches and standard deviation 1.5 inches, what percentage of women are between 58.5 inches and 64.5 inches?

A)49.9%
B)84.0%
C)2.1%
D)13.6%
E)81.9%

Question 12

Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities. P(x $\le$ 24) $\mu$ = 28; $\sigma$ = 5

A)0.788
B)0.394
C)0.144
D)0.288
E)0.212

Question 13

Find the area under the standard normal curve over the interval specified below. Between z = 0.8 and z = 1.9

A)-0.759
B)0.029
C)0.471
D)0.212
E)0.183

Question 14

Assuming that the heights of college women are normally distributed with mean 66 inches and standard deviation 2 inches, what percentage of women are shorter than 72 inches?

A)99.9%
B)0.1%
C)97.7%
D)2.3%
E)15.9%

Question 15

Find the area under the standard normal curve over the interval specified below. Between z = -2 and 1

A)0.819
B)0.477
C)0.341
D)0.499
E)0.136

Question 16

Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose for healthy females, x has an approximately normal distribution with mean $\mu$ = 4.3 and standard deviation $\sigma$ = 0.8 Convert the following x interval from a laboratory test to a z interval. 1.1 > x

A)-4 > z
B)1 < z
C)-4 < z
D)2 < z
E)4 < z

Question 17

Shade the area under the standard normal curve corresponding to the probability below. P(-1 $\le$ z $\le$ 0)

A)
B)
C)
D)
E)

Question 18

Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities. P(1 $\le$ x $\le$ 18) $\mu$ = 12; $\sigma$ = 4

A)0.997
B)0.067
C)0.106
D)0.930
E)0.003

Question 19

The incubation time for Rhode Island Red chicks is normally distributed with mean of 30 days and standard deviation of approximately 2 days. If 1000 eggs are being incubated, how many chicks do we expect will hatch in 26 to 36 days?

A)976 chicks
B)477 chicks
C)21 chicks
D)157 chicks
E)136 chicks

Question 20

Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose that for healthy females, x has an approximately normal distribution with mean $\mu$ = 4.7 and standard deviation $\sigma$ = 0.3 Convert the following x interval from a laboratory test to a z interval. 4.0 < x < 5.5

A)11.67 < z < 14.00
B)-4.00 < z < 14.00
C)-4.00 < z < -1.67
D)11.67 < z < 29.67
E)14.00 < z < 27.33

Question 21

Suppose that x has a distribution with $\mu$ = 21 and $\sigma$ = 5. If a random sample is taken of size n = 58, find . $$\mu _ { x } ^ { - }$$

A)5.00
B)0.66
C)2.76
D)13.81
E)21.00

Question 22

A person's level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean $\mu$ = 80 and standard deviation of $\sigma$ = 30 What is the probability that, for an adult after a 12-hour fast, x is less than 62?

A)0.226
B)0.274
C)0.137
D)0.363
E)0.726

Question 23

Assume that about 30% of all U.S. adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 140 insurance claims to be processed in the next few days. What is the probability that fewer than 38 of the claims have been padded?

A)0.259
B)0.797
C)0.741
D)0.770
E)0.203

Question 24

Find z such that 22.4% of the standard normal curve lies to the right of z.

A)0.759
B)-0.285
C)0.285
D)0.595
E)-0.759

Question 25

Select the graph corresponding to the following statement. 6.7% of the standard normal curve lies to the left of z.

A)
B)
C)
D)
E)

Question 26

Suppose that more than a decade ago high levels of lead in the blood put 78% of children at risk. A concerted effort was made to remove lead from the environment. Suppose, according to a survey, only 6% of children in the United States are at risk of high blood-lead levels. In a random sample of 150 children taken more than a decade ago, what is the probability that 105 or more had high blood-lead levels?

A)0.963
B)0.079
C)1.000
D)0.000

Question 27

Find z such that 24.1% of the standard normal curve lies to the left of z.

A)1.169
B)0.646
C)-0.703
D)-0.646
E)0.703

Question 28

A person's level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean $\mu$ = 78 and standard deviation of $\sigma$ = 25. What is the probability that, for an adult after a 12-hour fast, x is more than 49?

A)0.438
B)0.188
C)0.062
D)0.377
E)0.877

Question 29

What is a parameter?

A)A conclusion about the value of a population parameter based on information about the corresponding sample statistic and probability
B)A numerical descriptive measure of a population
C)A set of measurements (or counts), either existing or conceptual
D)A probability distribution for a sample statistic
E)A numerical descriptive measure of a sample

Question 30

Give an example of a population.

A)Seven cards chosen at random from a 52-card deck
B)A week of television shows watched by Americans as reported in a survey
C)The lengths of all trout in a lake
D)The automobiles bought by Americans polled in a telephone survey
E)Registered Oklahoma voters who voted in a U.S. presidential election

Question 31

Find z such that 40.3% of the standard normal curve lies between -z and z.

A)0.734
B)0.169
C)0.127
D)0.529
E)0.101

Question 32

A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 44 months and a standard deviation of 7 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

A)30 months
B)52 months
C)35 months
D)57 months

Question 33

Suppose that the average life of a refrigerator before replacement is $\mu$ = 14 years with a (99.7% of data) range from 8 to 20 years. Let x = age at which a refrigerator is replaced. Assume that x has a distribution that is approximately normal. Find a good approximation for the standard deviation of x values.

A)1 year
B)2 years
C)4 years
D)6 years
E)3 years

Question 34

A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 70 months and a standard deviation of 3.1 month. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for 50 million dollars. Assume that the only part of the satellite in question is the microchip. All other components will work indefinitely. If the satellite is insured for 71 months, what is the expected loss to the insurance company? Round to the nearest ten-thousand dollars.

A)$21.80 million
B)$31.32 million
C)$18.68 million
D)$6.32 million
E)$28.20 million

Question 35

The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a sample of ten 18-year-old men will be between 67 and 68 inches? $$\bar { x }$$

A)0.3531
B)0.6469
C)0.1469
D)0.7062
E)0.3961

Question 36

Suppose that x has a distribution with $\mu$ = 26 and $\sigma$ =6. If a random sample is taken of size n = 37, find $\sigma$ _x.

A)26.00
B)0.99
C)4.27
D)0.16
E)6.00

Question 37

The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the height of an 18-year-old man selected at random is between 70 inches and 71 inches?

A)0.9072
B)0.4072
C)0.0928
D)0.3008
E)0.1268

Question 38

What is a sampling distribution?

A)A conclusion about the value of a population parameter based on information about the corresponding sample statistic and probability
B)A numerical descriptive measure of a population
C)A set of measurements (or counts), either existing or conceptual
D)A probability distribution for a sample statistic
E)A numerical descriptive measure of a sample

Question 39

What is a statistic?

A)A conclusion about the value of a population parameter based on information about the corresponding sample statistic and probability
B)A numerical descriptive measure of a population
C)A set of measurements (or counts), either existing or conceptual
D)A probability distribution for a sample statistic
E)A numerical descriptive measure of a sample

Question 40

A person's level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean $\mu$ = 71 and standard deviation of $\sigma$ = 24. What is the probability that, for an adult after a 12-hour fast, x is between 35 and 110?

A)0.441
B)0.881
C)0.052
D)0.948
E)0.933

Question 41

Assume that about 30% of all U.S. adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 132 insurance claims to be processed in the next few days. What is the probability that from 31 to 47 of the claims have been padded?

A)0.843
B)0.891
C)0.871
D)0.899
E)0.911

Question 42

Suppose that about 25% of ice cream sales are vanilla and that about 8% of ice cream sales are chocolate. A customer who buys ice cream is not limited to one container or one flavor. What is the probability that someone who is buying ice cream will buy chocolate or vanilla? [Hint: Use the probability of success.]

A)0.330
B)0.310
C)0.020
D)0.080
E)0.350

Question 43

Suppose that about 62% of the people who are murdered actually knew the person who committed the murder. Suppose that a detective file in Boston has 62 current unsolved murders. What is the probability that fewer than 33 victims did not know their murderer?

A)0.995
B)0.007
C)0.993
D)0.010
E)0.990

Question 44

Assume that 53% of all customers will take free samples. Furthermore, of those who take the free samples, assume that about 32% will buy what they have sampled. Suppose that you set up a counter in a supermarket offering free samples of a new product and that the day you were offering free samples, 403 customers passed by your counter. What is the probability that a customer will take a free sample and buy the product? [Hint: Use the multiplication rule for dependent events. Notice we are given the conditional probability P(buy, given sample) = 0.32, while P(sample) = 0.53.]

A)0.320
B)0.604
C)0.210
D)0.170
E)0.530

Question 45

Assume that about 45% of all U.S. adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 102 insurance claims to be processed in the next few days. What is the probability that more than 49 of the claims are not padded?

A)0.947
B)0.957
C)0.906
D)0.888
E)0.065

Question 46

Suppose an airline found that about 3% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose that the airline overbooks this flight by selling 222 ticket reservations for an airplane with only 216 seats. Let n = 222 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. Which expression represents the probability that a seat will be available for everyone who shows up holding a reservation: Expression I: $\quad P ( r \geq 216 )$
Expression II: $\quad P ( r \geq 222 )$
Expression III : $\quad P ( r \leq 216 )$
Expression $T : P ( r \leq 222 )$
Expression $\mathrm { V } : \quad P ( r = 222 )$

A)Expression IV
B)Expression III
C)Expression II
D)Expression I
E)Expression V