1. 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)=

2. 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 91% 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 91% of all samples of size 20 is_______ pounds

3. Prison Sentences The average prison sentence for a person convicted of second-degree murder is 15

years. If the sentences are normally distributed with a standard deviation of 2.5 years, find the following probabilities. Round the final answers to at least four decimal places and intermediate z -value calculations to two decimal places.

a. A prison sentence is greater than 19 years.

P(x>19)=

b. A prison sentence is less than 12 years.

P(x<12)=