Instructions:

In this task, you will work with continuous probability distributions. You will explain the nature of the continuous probability distribution and its applications to practical situations. In addition, you will calculate the probabilities associated with the normal probability distribution. You must read the material presented in sections 6.2 and 6.3 of the textbook to complete the exercises assigned for this activity, which will assess your learning. You must present the processes necessary to support the answer of the exercises and round the final resultsnot the intermediate values that appear during the calculationsto two decimal places, when necessary.

Exercise 1

1) Mention three (3) important characteristics of the normal distribution. (3 points)

Exercise 2

1) Using the normal distribution table, answer: 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

2) The meat department at a local supermarket specifically prepares its "1 pound" packages of ground beef, so that there is a variety of weights; some slightly larger and some 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 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 weighs less than 0.80 pound? (2 points)

Exercise #4 based on Mendenhall, 2015

1. Studies have shown 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) The height of men is normally distributed, with a mean of 69.0 inches and a standard deviation of 2.8 inches. The height of women is normally distributed, with a mean of 63.6 inches and a standard deviation of 2.5 inches. Modeling academy rules require women to be taller than 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 Meteorology Center. Suppose 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)