Exercise #1

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

Exercise #2

Using the normal distribution table, he answers:

What is the probability that a random variable x is greater than 2.35?

a) less than -1.00 (2 points)

b) less than -2.50 (2 points)

c) greater than 1.25 (2 points)

d)between 1.00 and 2.00 (2 points)

e) between -1.8 and 2.8 (2 points)

f) greater than 3.22 (2 points)

g) less than -3.25 (2 points)

h) between -2.11 and 1.55 (2 points)

Exercise #3

The meat department at a local supermarket specifically prepares its "1 pound" packets of ground beef, so that there are a variety of weights; some, slightly larger, and others, slightly less than 1 pound. Suppose the weights of these "1 pound" packages are normally distributed with an average 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 one 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 will weigh less than 0.80 pounds? (2 points) Exercise #4 based on Mendenhall, 2015

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

Exercise #5

Men's height is normally distributed, with an average of 69.0 inches and a standard deviation of 2.8 inches. Women's height is normally distributed, with an average of 63.6 inches and a standard deviation of 2.5 inches. Modeling academy standards require women, to be models, to measure more than 66 inches (or 5 feet 6 inches). What percentage of women meet this requirement? (5 points)

Exercise #6

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

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

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

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