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.

Accepted Answer

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 .

Accepted Answer

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.

Accepted Answer

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.

Accepted Answer

The answer of The actual weight of the contents of...

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.

Accepted Answer

The answer of After finishing college, you start working as...

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.

Accepted Answer

The answer of After several weeks of compiling data you...

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.

Accepted Answer

The answer of The lung capacity of an Olympic swimmer...

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 ?

Accepted Answer

The answer of The graph below is of a normal...

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.

Accepted Answer

The answer of An honest coin is tossed a total...

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?

Accepted Answer

The answer of In a normal distribution with a standard...

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.

Accepted Answer

The answer of After several weeks of compiling data you...

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.

Accepted Answer

The answer of The battery life of an iPod has...

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 ?

Accepted Answer

The answer of The graph below is of a normal...

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.

Accepted Answer

The answer of The amount of time that a student...

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.

Accepted Answer

The answer of After finishing college, you start working as...

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?

Accepted Answer

The answer of In a normal distribution with a mean...

Question 17

A normal distribution has a mean of 80 and a standard deviation of . If the 2.5^th percentile is P_2.5=72 , then find the standard deviation .

Accepted Answer

The answer of A normal distribution has a mean of...

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.

Accepted Answer

The answer of An honest coin is tossed a total...

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.

Accepted Answer

The answer of The battery life of an iPod has...

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.

Accepted Answer

The answer of The lung capacity of an Olympic swimmer...

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

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

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.

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.

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.

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 16th percentile P16 ?

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.

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?

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.

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.

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 84th percentile P84 ?

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.

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?

A normal distribution has a mean of 80 and a standard deviation of . If the 2.5th percentile is P2.5=72 , then find the standard deviation .

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.

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.

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.

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 .

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 ?

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 ?

A normal distribution has a mean of 80 and a standard deviation of . If the 2.5^th percentile is P_2.5=72 , then find the standard deviation .