7.1 Normal distribution

Instructions:

In this task, you will work with the continuous probability distributions. You will explain the nature of the continuous probability distribution and its applications in practical situations. In addition, you will calculate the probabilities associated with the normal probability distribution.

You should present the processes necessary to support the answers to the exercises and round the final results not the intermediate values that appear during the calculations to two decimal places, when necessary.

1. What is the normal distribution for?

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 =

b) less than -2.30 =

c) greater than 1.45 =

d) between 1.00 and 2.10 =

e) between -1.7 and 2.8 =

f) greater than 3.26 =

g) less than -3.15 =

h) between -2.11 and 1.15 =

3. The meat department at a local grocery store specifically prepares their "1 pound" packages of ground beef, so there is a variety of weights; some slightly larger and some slightly less than 1 pound. Suppose the weights of these "1 pound" packages are normally distributed with a mean of 1.00 pounds and a standard deviation of .15 pounds (Mendenhall et al., 2015).

a.What proportion of the packages will weigh more than 1.5 pounds?

b. What proportion of the packages will weigh between 0.98 and 1.15 pounds? (2 points)

c. What is the probability that a randomly selected package of ground beef weighs less than .90 pounds?

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 38 miles per gallon (mpg) and a standard deviation of 3.5 mpg. What percentage of compacts get 45 mpg or more? (Mendenhall et al., 2015)

Exercise #5

1).... Men's height is normally distributed, with a mean of 69.0 inches and a standard deviation of 2.8 inches. Women's height is normally distributed, with a mean of 63.6 inches and a standard deviation of 2.5 inches. The United States military requires women to be between 58 and 80 inches tall.What percentage of women meet this requirement?

Exercise # 6

1) The average amount of rainfall in Puerto Rico during the past month was 4.5 inches, according to the National Meteorology Center. Suppose that a normal distribution can be used and that the standard deviation is 0.6 inches.

a...What percentage of the time was last month's rainfall greater than 6 inches?

b. What percentage of the time was rainfall less than 4 inches?

c. A month is considered extremely humid if the rainfall is 10% higher for that month. How much rainfall must be in April to be considered an extremely humid month?