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

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.

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

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 .

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.

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?

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

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.

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 4.5 hours and 5 hours? Give your answer as a percentage.

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.

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 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 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 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.

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.

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.

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.

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.

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.

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.