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# Statistics: understanding z-scores and probabilities of obse

I would like some help with the following problems. Can I please get the actual manual work for the problems so I can follow the formula and follow the steps with other word problems. Thanks.

1. A normal population has a mean of 20.0 and a standard deviation of 4.0.
a. compute the z value associated with 25.0.
b. what proportion of the population is between 20.0 and 25.0?
c. what proportion of the population is less than 18.0?

2. The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, with a mean of \$70,000 and a standard deviation of \$20,000. A loan application is received this morning.
What is the probability.
a. the amount requested is \$80,000 or more?
b. the amount requested is between \$65,000 and \$80,000?
c. the amount requested is \$65,000 or more?

3. A study found that a mean waiting time to see a physician at an outpatient clinic was 40 minutes with a standard deviation of 28 minutes. a. what is the probability of more than an hours wait.
b. less than 20 minutes.
c. at least 10 minutes.

4. the credit score of a 35 yr old applying for a mortgage at Ulysses Mortgage Associates is normally distributed with a mean of 600 and a standard deviation of 100.
a. find the credit score that defines the upper 5 percent.
b. seventy-five percent of the customers will have a credit score higher than what value?
c. within what range would the middle 80 percent of credit scores lie.

#### Solution Summary

A step by step solution to all the problems is provided. It shows how to find probabilities from a normal distribution.

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