Deck 17: The Mathematics of Normality: the Call of the Bell

Question 1

The actual weight of the contents of an 11-ounce bag of potato chips has an approximate normal
distribution with a mean of 11.6-ounces and a standard deviation of 0.2-ounces. What is the
probability of randomly picking a bag with an actual weight greater than 11.8-ounces? Give your
answer as a percentage.

Answer 1

16%

Question 2

A normal distribution has a mean of and a standard deviation of 12 . If the 84^th percentile is P=98 , then find the mean .

Answer 2

86

Question 3

The amount of time that a student brushes his teeth has an approximate normal distribution with a
mean of 1.8 minutes and a standard deviation of 0.3 minutes. What is the probability that the student
brushes his teeth for less than 1.5 minutes? Give your answer as a percentage.

Answer 3

16%

Question 4

The actual weight of the contents of an 11-ounce bag of potato chips has an approximate normal
distribution with a mean of 11.6-ounces and a standard deviation of 0.2-ounces. What is the
probability of randomly picking a bag with an actual weight more than 11.4-ounces? Give your
answer as a percentage.

Question 5

After finishing college, you start working as a quality control agent at a local manufacturing plant. The machine that you are in charge of produces steel bolts. Your job is to fine tune the machine so that it produces a specific size bolt, but a small margin of error is allowable. Suppose that you believe that the machine has been calibrated so that the actual size of a bolt produced has an approximate normal
distribution with a mean of 25 cm and a standard deviation of 0.001 cm. After producing 1000 bolts,
you randomly choose one and find that it measures 24.9995 cm. Based off of this measurement, do you think that the machine has been properly calibrated? Explain.

Question 6

After several weeks of compiling data you determine that 36% of emails that you receive are spam-
emails while the remaining 64% are not. Suppose that you receive 2500 emails in a week, what is the
probability that less than 876 of the emails are spam-emails? Give your answer as a percentage.

Question 7

The lung capacity of an Olympic swimmer has an approximate normal distribution with a mean of 9
liters and a standard deviation of 0.4 liters. What is the first quartile for lung capacity in this distribution? Round your answer to two decimal places.

Question 8

The graph below is of a normal curve. The shaded portion of the graph represents 95 % of the total area under the curve. According to the graph, what is the value of the 16^th percentile P₁₆ ?

Question 9

An honest coin is tossed a total of n = 1600 times and the number of heads obtained is recorded. What
is the probability that the coin lands heads greater than 840 times? Give your answer as a percentage.

Question 10

In a normal distribution with a standard deviation of 8, the number 83 has a standardized value of 2.5.
What is the mean of this normal distribution?

Question 11

After several weeks of compiling data you determine that 36% of emails that you receive are spam-
emails while the remaining 64% are not. Suppose that you receive 625 emails in a week, what is the
probability that between 201 and 225 of the emails are spam-emails? Give your answer as a
percentage.

Question 12

The battery life of an iPod has an approximate normal distribution with a mean of 6 hours and a
standard deviation of 0.5 hours. What is the probability that a randomly chosen iPod will have a
battery life between 4.5 hours and 5 hours? Give your answer as a percentage.

Question 13

The graph below is of a normal curve. The shaded portion of the graph represents 95 % of the total area under the curve. According to the graph, what is the value of the 84^th percentile P₈₄ ?

Question 14

The amount of time that a student brushes his teeth has an approximate normal distribution with a
mean of 1.8 minutes and a standard deviation of 0.3 minutes. What is the probability that the student
brushes his teeth for less than 1.2 minutes? Give your answer as a percentage.

Question 15

After finishing college, you start working as a quality control agent at a local manufacturing plant. The machine that you are in charge of produces steel bolts. Your job is to fine tune the machine so that it produces a specific size bolt, but a small margin of error is allowable. Suppose that you believe that the machine has been calibrated so that the actual size of a bolt produced has an approximate normal
distribution with a mean of 25 cm and a standard deviation of 0.001 cm. After producing 1000 bolts,
you randomly choose one and find that it measures 25.008 cm. Based off of this measurement, do you think that the machine has been properly calibrated? Explain.

Question 16

In a normal distribution with a mean of 18, the number 25 has a standardized value of 1.6. What is the standard deviation of this normal distribution?

Question 17

A normal distribution has a mean of 80 and a standard deviation of https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/. If the 2.5^th percentile is P_2.5=72 , then find the standard deviation .

Question 18

An honest coin is tossed a total of n = 3600 times and the number of heads obtained is recorded. What
is the probability that the coin lands heads less than 1860 times? Give your answer as a percentage.

Question 19

The battery life of an iPod has an approximate normal distribution with a mean of 6 hours and a
standard deviation of 0.5 hours. What is the probability that a randomly chosen iPod will have a
battery life between 5 hours and 6.5 hours? Give your answer as a percentage.

Question 20

The lung capacity of an Olympic swimmer has an approximate normal distribution with a mean of 9
liters and a standard deviation of 0.4 liters. What is the third quartile for lung capacity in this
distribution? Round your answer to two decimal places.

Question 21

The time that it takes an Olympic runner to finish the 100-meter dash is approximately normal with a mean of 9.83 seconds with a standard deviation of 0.06 seconds. What is the probability it would take The runner less than 10.01 seconds to finish the race? Give your answer as a percentage.

A) 0.15%
B) 95%
C) 99.7%
D) 99.85%
E) None of the above.

Question 22

The graph below is of a normal curve. The shaded portion of the graph represents 68 % of the total area under the curve. According to the graph, what is the value of the 99.85^th percentile P_99.85 ?

A) 35
B) 47
C) 53
D) 59
E) None of the above.

Question 23

A local church lottery states that the probability that any ticket wins a prize is 36%. Suppose that you are generous and purchase 1225 tickets, what is the probability that more than 441 of the tickets result In a prize? Give your answer as a percentage.

A) 36%
B) 50%
C) 64%
D) 68%
E) None of the above.

Question 24

The height of an 18-year old student at your university has an approximate normal distribution with a mean of 68 inches and a standard deviation of 2.5 inches. What is the first quartile of height in this Distribution? Round your answer to two decimal places.

A) 25 inches
B) 66.31 inches
C) 67.25 inches
D) 69.34 inches
E) None of the above.

Question 25

A normal distribution has a mean of and a standard deviation of . Suppose that you know that 2.5^th percentile P₂₅=8 and the 84^th percentile P₈₄=29 . Find the mean of this normal distribution.

A) 7
B) 13
C) 18
D) 22
E) None of the above.

Question 26

An honest six-sided die is tossed a total of n = 324 times and the number of times that the die lands on an even number (2, 4, or 6) is recorded. What is the probability that between 144 and 171 of the tosses Result in an even number? Give your answer as a percentage.

A) 61%
B) 81.5%
C) 95%
D) 99.7%
E) None of the above.

Question 27

The time that it takes an Olympic runner to finish the 100-meter dash is approximately normal with a mean of 9.83 seconds with a standard deviation of 0.06 seconds. What is the probability it would take The runner more than 9.89 seconds to finish the race? Give your answer as a percentage.

A) 2.5%
B) 5%
C) 16%
D) 34%
E) None of the above.

Question 28

The graph below is of a normal curve. The shaded portion of the graph represents 68% of the total area under the curve. According to the graph, what is the value of the 97.5th percentile P97.5 ?

A) 2
B) 3
C) 12
D) 35
E) None of the above.

Question 29

The actual number of hours that a candle will burn has an approximate normal distribution with a mean of 18 hours and a standard deviation of 1.2 hours. What is the probability that the candle will burn for Less than 15.6 hours? Give your answer as a percentage.

A) 2.5%
B) 5%
C) 16%
D) 95%
E) None of the above.

Question 30

The time that it takes a student to walk from his dorm room to his math classroom has an approximate normal distribution with a mean of 8 minutes and a standard deviation of 0.4 minutes. What is the Probability that the student will take between 8.4 and 9.2 minutes to walk to class? Give your answer As a percentage.

A) 2.5%
B) 15.85%
C) 95%
D) 99.7%
E) None of the above.

Question 31

A local church lottery states that the probability that any ticket wins a prize is 36%. Suppose that you are generous and purchase 1225 tickets, what is the probability that less than 441 of the tickets result in A prize? Give your answer as a percentage.

A) 25%
B) 34%
C) 68%
D) 95%
E) None of the above.

Question 32

Which of the following scenarios would it not be appropriate to model with a normal distribution?

A) Height of an 18-year old male student at your university.
B) Actual weight of the contents of a 12-ounce can of dog food.
C) Number of fingers on the left hand of an 18-year female student at your university.
D) Verbal SAT score of a recent high school graduate.
E) None of the above.

Question 33

The actual number of hours that a candle will burn has an approximate normal distribution with a mean of 18 hours and a standard deviation of 1.2 hours. What is the probability that the candle will burn for Less than 14.4 hours? Give your answer as a percentage.

A) 0.15%
B) 2.5%
C) 15.85%
D) 99.7%
E) None of the above.

Question 34

A normal distribution has a mean of and a standard deviation of . Suppose that you know that 16^th percentile P₁₆=23 and the 97.5^th percentile P_97.5=62 . Find the mean of this normal distribution.

A) 36
B) 38
C) 41
D) 47
E) None of the above.

Question 35

The time that it takes a student to walk from his dorm room to his math classroom has an approximate normal distribution with a mean of 8 minutes and a standard deviation of 0.4 minutes. What is the Probability that the student will take between 8.0 and 9.2 minutes to walk to class? Give your answer As a percentage.

A) 0.3%
B) 2.5%
C) 49.85%
D) 34%
E) None of the above.

Question 36

Which of the following scenarios would it be appropriate to model with a normal distribution?

A) Height of an 18-year old male student at your university.
B) Gender of an individual attending a hockey game.
C) Number of fingers on the left hand of an 18-year female student at your university.
D) Scores on an exam in which everyone received a 100%.
E) None of the above.

Question 37

In a normal distribution with a mean of 30 , the number 45 has a standardized value of 1.2 . What is the 16^th percentile P₁₆ of this normal distribution?

A) 16
B) 17.5
C) 21.5
D) 27.6
E) None of the above.

Question 38

In a normal distribution with a standard deviation of 8 , the number 25 has a standardized value of -2.5 . What is the 84^th percentile P₈₄ of this normal distribution?

A) 45
B) 53
C) 62
D) 84
E) None of the above.

Question 39

The height of an 18-year old student at your university has an approximate normal distribution with a mean of 68 inches and a standard deviation of 2.5 inches. What is the third quartile of height in this Distribution? Round your answer to two decimal places.

A) 63 inches
B) 65.5 inches
C) 69.69 inches
D) 72.42 inches
E) None of the above.

Question 40

An honest six-sided die is tossed a total of n = 324 times and the number of times that the die lands on an even number (2, 4, or 6) is recorded. What is the probability that between 162 and 171 of the tosses Result in an even number? Give your answer as a percentage.

A) 16%
B) 34%
C) 68%
D) 99.7%
E) None of the above.