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

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 ?

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.

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 ?

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?

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.

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.

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.

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.

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.

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.

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?

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 mean of 18, the number 25 has a standardized value of 1.6. What is the standard deviation 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 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.

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 .

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.

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 ?

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.

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.

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.