Exercise 1

List three (3) important features of the normal distribution. (3 points)

Exercise 2

Using the normal distribution table, answer: What is the probability that a random variable x is greater than 2.35?

less than -1.00 (2 points)

less than -2.50 (2 points)

greater than 1.25 (2 points)

between 1.00 and 2.00 (2 points)

between -1.8 and 2.8 (2 points)

greater than 3.22 (2 points)

less than -3.25 (2 points)

between -2.11 and 1.55 (2 points)

Exercise 3

The meat department at a local supermarket specifically prepares their "1 pound" packages of ground beef, so there is a variety of weights; some slightly larger and others slightly less than 1 pound. Assume that the weights of these "1-pound" packages are normally distributed with a mean of 1.25 pounds and a standard deviation of 0.20 pounds (Mendenhall et al., 2015).

A) What proportion of the packages will weigh more than a pound? (2 points)

B) What proportion of the packages will weigh between 0.95 and 1.05 pounds? (2 points)

C) What is the probability that a randomly selected package of ground beef weighs less than 0.80 pound? (2 points)

Exercise #4

1. Studies show that gasoline use for compact cars sold in the United States is normally distributed, with a mean of 36.5 miles per gallon (mpg) and a standard deviation of 5.5 mpg. What percentage of compacts get 35 mpg or more? (Mendenhall et al., 2015) (4 points)

Exercise #5

1) Male heights are normally distributed, with a mean of 69.0 inches and a standard deviation of 2.8 inches. Women's heights are normally distributed, with a mean of 63.6 inches and a standard deviation of 2.5 inches. Modeling academy regulations require women to be over 66 inches (or 5 feet 6 inches) to be models. What percentage of women meet this requirement? (5 points)

exercise #6

1) The average amount of rainfall in Puerto Rico during the past month was 3.5 inches, according to the National Weather Center. Assume that a normal distribution can be used and that the standard deviation is 0.8 inches.

A. What percentage of the time last month's rainfall was greater than 4 inches? (3 points)

b. What percentage of the time was the rainfall less than 3 inches? (3 points)

c. A month is considered extremely wet if the rainfall is 10% higher for that month. How much rainfall must be in April for it to be considered an extremely wet month? (3 points)