1. SupposeZfollows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places.

a. P(Z1.58) =

b. P(Z>1.86) =

c. P (-0.88

2.SupposeZfollows the standard normal distribution. Use the calculator provided, orthis table, to determine the value ofc so that the following is true.

P(-cZc) = 0.9512

Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

3. SupposeZ follows the standard normal distribution. Use the calculator provided, orthis table, to determine the value ofcso that the following is true

P(cZ-0.91) = 0.1368

Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

5. According to her doctor, Mrs. Barnes's cholesterol level is higher than only5% of the females aged50 and over. The cholesterol levels among females aged 50and over are approximately normally distributed with a mean of230mg/dL

and a standard deviation of25mg/dL.What is Mrs. Barnes's cholesterol level? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

___ mg/dL

6. A psychologist has designed a questionnaire to measure individuals' aggressiveness. Suppose that the scores on the questionnaire are normally distributed with a standard deviation of100. Suppose also that exactly10%of the scores exceed700. Find the mean of the distribution of scores. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

7. An aptitude test is designed to measure leadership abilities of the test subjects. Suppose that the scores on the test are normally distributed with a mean of580and a standard deviation of120. The individuals who exceed780on this test are considered to be potential leaders. What proportion of the population are considered to be potential leaders? Round your answer to at least four decimal places.

8. Suppose that 53%of the population of U.S. voters favors a particular presidential candidate. If a random sample of55voters is chosen, approximate the probability that at least28favor this candidate. Use the normal approximation to the binomial with a correction for continuity.

Round your answer to at least three decimal places. Do not round any intermediate steps.

9. The mean starting salary offered to graduating students with a certain major in a recent year was$64,245, with a standard deviation of$3712. A random sample of 75of that year's graduating students with the major has been selected.

What is the probability that the mean starting salary offered to these 75students was$64,000or less?

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

10. According to previous studies,10%of the U.S. population is left-handed. Not knowing this, a high school student claims that the percentage of left-handed people in the U.S. is12%.

The student is going to take a random sample of900people in the U.S. to try to gather evidence to support the claim. Letpbe the proportion of left-handed people in the sample.

Answer the following.

a. Find the mean ofp.

b. Find the standard deviation ofp

c. Compute an approximation forP(p0.12)which is the probability that there will be12%or more left-handed people in the sample. Round your answer to four decimal places.