Normal Probabilities Using a Table

Find the area under the standard normal curve where z < 2.42 .

• .008

• .992

• .301

• .862

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

A franchisor records monthly profits (in £) from each of its 180 franchisees. Sales for the most recent month are given in the table below. To advertise its franchise the franchisor would lke to publish probabilities that a franchisee can hope to earn for each of several profit brackets. To calculate these probabilities, the franchisor models profits as following a normal distribution. Is the normal distribution an appropriate model to use, given the data in the table? [From the raw data, the sample mean profit is £1843.17, and the sample standard deviation is £643.63.] To give a solution, ANSWER the following questions. The null and alternative hypotheses are:

Find the area under the standard normal distribution curve.

  Between z = 0 and z = 1.77

Find the area under the standard normal distribution curve.

To the right of z = 0.37

Find the area under the standard normal distribution curve.

To the left of z = −0.75

Find the probabilities for each, using the standard normal distribution.

P(0 < z < 0.95)

Find the probabilities for each, using the standard normal distribution.

P(z > 2.33)

Find the z value that corresponds to the given area.

Area=0.9671

Note: You will see 3 variations of this question. Also, Use the Table given in class, Nspire solutions do not match

Monthly Mortgage Payments The average monthly mortgage payment including principal and interest is $982 in the United States. If the standard deviation is approximately $180 and the mortgage payments are approximately normally distributed, find the probability that a randomly selected monthly payment is

a.    More than $1000