Deck 5: A Normal World

Question 1

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.

Answer 1

121.6, 150.4

Question 2

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 mean test score of the sample is computed. What percentage of sample means are less than 70?

A) 19.46%
B) 12.85%
C) 2.87%
D) 13.46%

Answer 2

2.87%

Question 3

The amount of Jen's monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.

Answer 3

about $43.30

Question 4

Which of the following statements concerning the standard normal curve is/are true (if any)? a. The area under the standard normal curve to the left of −3 is zero.
B) The area under the standard normal curve between any two z-scores is greater than zero.
C) The area under the standard normal curve between two z-scores will be negative if both
Z-scores are negative.
D) The area under the standard normal curve to the left of any z-score is less than 1.

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

Question 5

Select the distribution that appears to be the most normal.

A)

B)

C)


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

Question 6

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.25 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.24 inches?

Question 7

The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 460 pencils, approximately how many would you expect to have a diameter less than 0.293 inches?

Question 8

The amount of Jen's monthly electric bill is normally distributed with a mean of $160 and a standard deviation of $14. Fill in the blanks.
95% of her electric bills are between $_____ and $_____.

Question 9

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, use the 68-95-99.7 rule to approximate the percentage of light bulbs having a life between 2000 hours and 3500 hours?

A) About 13.5%
B) About 50%
C) About 68%
D) About 81.5%

Question 10

Which of the following statements concerning areas under the standard normal 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, c
B) b, c
C) a, b
D) a

Question 11

The weights of a large population of male students have a mean of 160 pounds with a standard deviation of 15 pounds. What is the mean of the distribution of sample means for samples of 16 students?

Question 12

The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

Question 13

The lifetimes of projector bulbs of a particular type are normally distributed with a mean of 470 hours and a standard deviation of 15 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?

Question 14

Decide which of the described variables likely have a normal or near-normal distribution.
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 number of heads that show when two coins are tosses

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

Question 15

At one college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.

Question 16

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 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 90.8 inches?

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

Question 17

Select the distribution that appears to be the most normal.

A)


B)


C)



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

Question 18

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

A) About 25%
B) About 50%
C) About 75%
D) About 68%

Question 19

The annual precipitation for one city is normally distributed with a mean of 72 inches and a standard deviation of 3.5 inches. Fill in the blanks.
In 99.7% of the years, the precipitation in this city is between _____ and _____ inches.

Question 20

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 270 hours and a standard deviation of 11 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations of the mean on either side?

Question 21

Which set of data represented by the three histograms below most likely came from a normal distribution?

A)


B)


C)

Question 22

The scores on a certain test are normally distributed with a mean score of 58 and a standard deviation of 4. What is the likelihood that a sample of 90 students will have a mean score of at least 58.4216?

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

Question 23

Decide which of the described variables is/are likely have a normal or near-normal distribution.
a. The heights of corn stalks in one row of corn that is half a mile long
b.The numbers of viewers of each of the channels from 202 to 550 on Direct TV at 7:00
PM CDT on the third Thursday of November 2012 (349 data values)

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

Question 24

Standard used car prices are based on the assumption that a car will be driven an average of 12,000 miles per year. If the standard deviation is 2000 miles, approximately what percent of cars will be driven between 8000 and 16,000 miles per year?

Question 25

Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the 60th percentile.

Question 26

Which one of the three variables below is most likely to be normally or nearly normally distributed?

A) The results of throwing a die 1000 times
B) The lengths of randomly selected white pine needles
C) The number of people standing in line at five cash registers

Question 27

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 mean times are normally distributed, what percentage of sample means are greater than 9.1 hours?

A) 65.54%
B) 34.46%
C) 0.62%
D) 99.38%

Question 28

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard
deviation of 500 hours, what percent of the bulbs will not last as long as 2000 hours?
Apply the 68-95-99.7 rule to answer #4 and #5.

Question 29

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?

A) About 84%
B) About 68%
C) About 32%
D) About 16%

Question 30

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 8. What is the mean of the distribution of sample means with a sample size of 9?

Question 31

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. If an applicant is randomly selected, find the probability of a rating that is between 225 and 275.

Question 32

Apply the 68-95-99.7 rule to answer

-The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks. in 95% of the years, the precipitation in this city is between _____ and _____ inches.

Question 33

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

Question 34

There are over 1200 species of inchworms indigenous to North America. Some have been taken to the space station while others provided the idea for neon inchworms from the Jelly Belly Candy Company. One species has a mean length of 0.98 inches and a standard deviation of 0.05 inches. The lengths of 99.7% of these worms will be between ________ and _________ inches.

Question 35

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 mean times are normally distributed, what percentage of sample means are greater than 7.7 hours?

A) 0.62%
B) 34.46%
C) 65.54%
D) 99.38%

Question 36

The area under the standard normal 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
B) b, c
C) d
D) e
E) a, b

Question 37

Apply the 68-95-99.7 rule to answer

-The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg. What percentage of 18-year-old women have a systolic blood pressure that is within 3 standard deviations of the mean on either side?

Question 38

A math teacher gives two different tests to measure students' aptitude for math. Scores on the first test are normally distributed with a mean of 24 and a standard deviation of 4.5. Scores on the second test are normally distributed with a mean of 70 and a standard deviation of 11.3.
Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.)

Question 39

The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 6. If 9 fish are randomly selected, what is the likelihood that the mean weight will be between 17.6 and 21.6 lb?

A) 0.9370
B) 0.6800
C) 0.6730
D) 0.0968

Question 40

Select the distribution that appears to be the most normal.

A)

B)

C)

Question 41

Which of the following two or more statements about the standard normal distribution are always true?
A) If b is less than c, then the area to the left of b is less than the area to the left of c.
B) If a z-score is negative, then the area to the left of the z-score is negative.
C) If a z-score is positive, then the area to the right of the z-score is positive.
D) If the area to the right of a z-score is positive, then the z-score is positive.

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

Question 42

Assuming that the lengths of the inchworms in Problem 5 are normally distributed, find the 80th percentile of the lengths.

Question 43

A rocket club makes its own rockets. The rockets go to a mean height of 1100 feet with a standard deviation of 60 feet. If the club fires 36 rockets, what is probability that the mean height of the rockets will be greater than 1080 feet?

Question 44

Salesmen for the ABC Plastics Company drive an average of 240 miles per day with a standard deviation of 36 miles. If samples of 25 daily mileages are taken, what is the standard deviation of the distribution of sample means?

Question 45

For a randomly selected inchworm from a normal population with mean 0.98 inches and standard deviation 0.05 inches, find the probability that its length will be between 0.93 inches and 1.02 inches.

Question 46

Many colleges require SAT scores of high school students for admission. The scores on each part of the test range from 200 to 800. In one year, the mean verbal score was 431 with a standard deviation of 119, while the mean mathematical score was 472 with a standard deviation of 128. Find the percentile for a verbal score of 550. Then find the score on the mathematics portion of the test that has the same percentile.

Question 47

The mean life of a set of AAA batteries used in a handheld GPS (Global Positioning System) unit is 8 hours with a standard deviation of 0.5 hours. Assuming that the battery lives are normally distributed, if a class uses 16 of these units on a field trip, approximately how many will still be working after 8.25 hours?