Deck 5: A Normal World

Question 1

Estimate the percentage of light bulbs having a life between 2000 hours and 3000 hours.

A)50%
B)70%
C)20%
D)30%

Answer 1

B

Question 2

Estimate (using area)the relative frequency of values between 2000 hours and 2500 hours.

A)0.35
B)0.65
C)0.15
D)0.5

Answer 2

A

Question 3

Decide which of the data sets you would expect to be normally distributed

-a. The number of courses remaining until graduation for the students
In a small liberal arts college
B. The heights of male students in an advanced placement mathematics
Class
C. The SAT mathematics scores for students in an advanced placement
Mathematics class

A)b
B)a
C)c
D)none

Answer 3

b

Question 4

Use the following distribution to answer the question.
What is the mean of the distribution?

A)2500
B)4000
C)3000
D)2000

Question 5

Decide which of the data sets you would expect to be normally distributed

-a. The exact weights of a random sample of DVDs from the same manufacturer
B. The body temperatures of the students at the local university

A)b
B)both
C)a
D)neither

Question 6

Decide which of the data sets you would expect to be normally distributed

-a. The amount of change held by a teacher at the end of each
Day for a year
B. The amount of pocket money held by each student at a
Mid-sized liberal arts college at a given time
C. The amount of property taxes paid by homeowners in a
New "affordable housing" subdivision

A)a
B)c
C)none
D)b

Question 7

Apply the 68-95-99.7 rule to answer the question.

-The lifetimes of light bulbs of a particular type are normally distributed with a mean of 310 hours and a standard deviation of 9 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations to either side of the mean?

A)98%
B)68%
C)95%
D)99.7%

Question 8

Decide which of the data sets you would expect to be normally distributed

-a. The heights of the fans at a highly anticipated basketball game
B. The viewership of channels 202 to 550 on Direct TV at 7:00 PM CDT
On the third Thursday in August 2000

A)a
B)both
C)b
D)neither

Question 9

Select the appropriate distribution.

-Select the distribution that appears to be closest to normal.

A)


B)


C)


D) None of the distributions appear to be normal or near-normal.

Question 10

Use the following distribution to answer the question.
What is the total area under the curve?

A)3
B)2500
C)3000
D)1

Question 11

Select the appropriate distribution.
Select the distribution that appears to be closest to normal.

Question 12

Decide which of the data sets you would expect to be normally distributed

-a. The amount of income taxes paid by residents of a wealthy neighborhood
B. The results from 1000 spins of a spinner with 4 equally likely outcomes

A)a
B)both
C)neither
D)b

Question 13

Apply the 68-95-99.7 rule to answer the question.
The lifetimes of light bulbs of a particular type are normally distributed with a mean of 350 hours and a
Standard deviation of 6 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation
To either side of the mean?

A)68%
B)32%
C)84%
D)95%

Question 14

Apply the 68-95-99.7 rule to answer the question.

-The systolic blood pressure of a group of 18-year-old women is normally distributed with a mean of 113 mmHg and a standard deviation of 13 mmHg. What percentage of 18-year-old women in this group have a Systolic blood pressure that lies within 3 standard deviations to either side of the mean?

A)34%
B)95%
C)99.7%
D)68%

Question 15

Estimate (using area)the relative frequency of values greater than 2500 hours.

A)0.05
B)0.5
C)0.15
D)0.85

Question 16

Select the appropriate distribution.
Select the distribution that appears to be closest to normal.

Question 17

Select the appropriate distribution.
Select the distribution that appears to be closest to normal.

Question 18

Estimate the percentage of light bulbs having a life less than 3000 hours.

A)50%
B)30%
C)15%
D)85%

Question 19

Apply the 68-95-99.7 rule to answer the question.

-The systolic blood pressure of a group of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women in this group have a systolic blood pressure between 108 mmHg and 132 mmHg?

A)99.7%
B)68%
C)50%
D)95%

Question 20

Decide which of the data sets you would expect to be normally distributed

-a. The occurrence of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 in
Social security numbers
B. The number of siblings of the students attending
Bloomington High school on the 10th day of attendance
For the 2000-2001 school year

A)neither
B)b
C)both
D)a

Question 21

Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary.

-A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and astandard deviation of 50. What percentage of the ratings will be between 200 and 300?

A)95%
B)47.27%
C)97.72%
D)47.72%

Question 22

Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary.

-The volumes of soda in quart soda bottles are normally distributed with a mean of 32 ounces and a standard deviation of 1.2 ounces. What percentage of soda bottles will have a volume less than 31.46 ounces?

A)68%
B)67.36%
C)36.24%
D)32.64%

Question 23

Apply the 68-95-99.7 rule to answer the question.

-The annual precipitation for one city is normally distributed with a mean of 266 inches and a standard deviationof 2.5 inches. What percentage of years had precipitation between 261 inches and 271 inches?

A)99.7%
B)34%
C)68%
D)95%

Question 24

Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary.

-The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a human pregnancy lasts at least 289 days?

A)91.92%
B)8.08%
C)8.80%
D)99.7%

Question 25

Find the requested mean or standard deviation.

-The heights of a large population of students have a mean of 60" with a standard deviation of 4". What is the mean of the resulting distribution of sample means for n =16?

A)15"
B)60"
C)30"
D)45"

Question 26

Solve the problem.

-The area under the standard normal distribution curve between 1 and 2 is equal to 0.1359. Scores on a particular aptitude test are normally distributed with a mean of 100 and a standard deviation of 10. Which of the following are equal to 13.59%?
A. The percentage of scores between 120 and 130
B. The percentage of scores between 110 and 120
C. The percentage of scores between 80 and 90
D. The percentage of scores between 90 and 120
E. The percentage of scores between 90 and 110

A)b, c
B)e
C)a, b
D)b

Question 27

Find the requested percentile.

-At one college, GPA's are normally distributed with a mean of 2.6 and a standard deviation of 0.6. Find the 75th percentile. Round your answer to one decimal place.

A)2.9
B)3.1
C)2.2
D)3

Question 28

Find the requested percentile.

-One college requires that scholarship students maintain a GPA of 3.3, when the GPAs at that college are normally distributed with a mean of 3.0 and a standard deviation of 0.6. What percentile must scholarship students
Remain in?

A)Approximately 80th percentile
B)Approximately 25th percentile
C)Approximately 31th percentile
D)Approximately 69th percentile

Question 29

Apply the 68-95-99.7 rule to answer the question.

-At one college, GPA's are normally distributed with a mean of 2.8 and a standard deviation of 0.5. What percentage of students at the college have a GPA between 2.3 and 3.3?

A)99.7%
B)84%
C)95%
D)68%

Question 30

Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary.

-The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

A)2.28%
B)95%
C)50%
D)97.72%

Question 31

Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary.

-Assume that the weights of nickels are normally distributed with a mean of 5.000 grams and a standard deviation of 0.06 grams. A vending machine will reject all coins with weights more than 1 standard deviation above or below the mean. What percentage of legal nickels will be rejected by the machine?

A)68%
B)5%
C)0.3%
D)32%

Question 32

Apply the 68-95-99.7 rule to answer the question.

-The annual precipitation for one city is normally distributed with a mean of 35.4 inches and a standard deviation of 3.9 inches. What percentage of years had precipitation between 23.7 inches and 47.1 inches?

A)99.7%
B)34%
C)95%
D)68%

Question 33

Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary.

-A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. What percentage of the ratings will be between 180 and 210?

A)23.47%
B)34.46%
C)57.93%
D)95%

Question 34

Find the requested percentile.

-Scores on an English test are normally distributed with a mean of 31.7 and a standard deviation of 6.6. Find the 41st percentile. Round your answer to one decimal place.

A)33.2
B)30.2
C)27.8
D)35.6

Question 35

Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary.

-The monthly incomes of trainees at a local mill are normally distributed, with a mean of $1,100 and a standard deviation $150. What percentage of trainees earn less than $875 a month?

A)93.32%
B)99.7%
C)6.68%
D)6.86%

Question 36

Apply the 68-95-99.7 rule to answer the question.

-The amount of Jen's monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. What percentage of her phone bills are between $40 and $60?

A)34%
B)99.7%
C)95%
D)68%

Question 37

Find the requested percentile.

-The weights of certain machine components are normally distributed with a mean of 8.62 grams and a standard deviation of 0.09 grams. Find the 97th percentile. Round your answer to one decimal place.

A)8.6 grams
B)8.7 grams
C)8.9 grams
D)8.8 grams

Question 38

Apply the 68-95-99.7 rule to answer the question.

-The amount of Jen's monthly phone bill is normally distributed with a mean of $78 and a standard deviation of $10. What percentage of her phone bills are between $48 and $108?

A)99.9%
B)95%
C)68%
D)99.7%

Question 39

Solve the problem.
Which of the following statements concerning areas under the standard normal distribution curve is/are true (if any)?
A. The area to the left of -3 in a standard normal distribution curve is zero.
B. The area under a standard normal distribution curve between any two z-scores is greater thazn ero.
C. The area under the standard normal normal distribution curve between two z-scores will be negative if
Both z-scores are negative.
D. The area under the standard normal distribution curve to the left of any z-score is less than 1.

A)a, c
B)a, b
C)b, d
D)a

Question 40

Solve the problem.
Which of the following statements concerning areas under the standard normal distribution curve is/are true?
A. If a z-score is negative, the area to its right is greater than 0.5
B. If the area to the right of a z-score is less than 0.5, the z-score is negative.
C. If a z-score is positive, the area to its left is less than 0.5

A)a
B)b, c
C)a, b
D)a, c

Question 41

The weights of the fish in a certain lake are normally distributed with a mean of 15 lb and a standard deviation of 6. If 4 fish are randomly selected, what is the likelihood that the mean weight will be between 12.6 and 18.6 Lb?

A)0.0968
B)0.3270
C)0.6730
D)0.4032

Question 42

Find the requested mean or standard deviation.

-The heights of a large population of students have a mean of 64" with a standard deviation of 6". What is the standard deviation of the resulting distribution of sample means for n =16 ?

A)1.5"
B)64"
C)16"
D)6"

Question 43

Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as
a percent rounded to hundredths of a percent.

-A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.77 hours. Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the rebuilding times are normally distributed, what percentage of sample means are greater than 8.0 hours?

A)91.92%
B)94.52%
C)5.48%
D)8.08%

Question 44

The scores on a certain test are normally distributed with a mean score of 51 and a standard deviation of 2. What is the likelihood that a sample of 90 students will have a mean score of at least 51.2108?

A)0.1587
B)0.3174
C)0.3413
D)0.8413

Question 45

Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as
a percent rounded to hundredths of a percent.

-A final exam in Math 160 has a mean of 73 with standard deviation 8.16. Assume that a random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed,
What percentage of sample means are greater than 78?

A)0.26%
B)99.87%
C)0.13%
D)99.74%

Question 46

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and astandard deviation of 50. If 70 different applicants are randomly selected, find the likelihood that their mean is above 215.

A)0.0026
B)0.0062
C)0.9938
D)0.9398

Question 47

Find the requested mean or standard deviation.

-The mean score on the exit examination for an urban high school is 63 with a standard deviation of 6. What is the standard deviation of the resulting distribution of sample means for n = 9?

A)2
B)9
C)6
D)21

Question 48

Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the likelihood that their mean body temperature will be less than 98.60°F.

A)0.0260
B)0.9497
C)0.9974
D)0.0026

Question 49

Find the requested mean or standard deviation.

-The mean score on the exit examination for an urban high school is 63 with a standard deviation of 7. What is the mean of the resulting distribution of sample means for n = 9?

A)63
B)7
C)9
D)21

Question 50

Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as
a decimal rounded to four decimal places.

-The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 72 inches, and a standard deviation of 12 inches. What is the likelihood that the mean annual snowfall during 36 randomly
Picked years will exceed 74.8 inches?

A)0.0026
B)0.5808
C)0.4192
D)0.0808

Question 51

Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as
a percent rounded to hundredths of a percent.

-A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed,
What percentage of sample means are less than 76?

A)2.87%
B)97.13%
C)66%
D)34%

Question 52

Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as
a decimal rounded to four decimal places.

-The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 84 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during
25 randomly picked years will be less than 86.8 inches?

A)0.9192
B)0.5808
C)0.0808
D)0.4192

Question 53

Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as
a percent rounded to hundredths of a percent.

-The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.Assume that a random sample of 25 pregnant woman is selected and the mean is computer. What percentage of sample means will be between 265 and 271 days?

A)99.74%
B)15.87%
C)68.26%
D)84.13%

Question 54

Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as
a percent rounded to hundredths of a percent.

-A final exam in Math 160 has a mean of 73 with standard deviation 9.8. Assume that a random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed,
What percentage of sample means are between 72 and 74?

A)30.85%
B)69.15%
C)38.3%
D)61.7%