1. Assume that z scores are normally distributed with mean of 0 and a standard deviation of 1. If =P<a<za0.3616, find a.

2. Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.

The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.2 years and a standard deviation of 1.9 years. Random samples of size 19 are drawn from the population and the mean of each sample is determined.

3. Small Business Owners Seventy-six percent of small business owners do not have a college degree. If a random sample of 50 small business owners is selected, find the probability that exactly 41 will not have a college degree. Round the final answer to at least 4 decimal places and intermediate z -value calculations to 2 decimal places.

P(X=41)=

4. Breaking Strength of Steel Cable The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds. A sample of 20 cables is selected and tested. Find the sample mean that will cut off the upper 82% of all samples of size 20 taken from the population. Assume the variable is normally distributed. Round intermediate z -value calculations to 2 decimal places and round the final answer to at least 2 decimal places.

The sample mean that will cut off the upper 82% of all samples of size 20 is