1. Find two z values, one positive and one negative, that are equidistant from the mean so that the areas in the two tails total 5%. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to four decimal places, separated by a comma if needed.

Z=

2. Qualifying Test Scores To qualify for a medical study, an applicant must have a systolic blood pressure in the 50% of the middle range. If the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 3, find the upper and lower limits of blood pressure a person must have to qualify for the study. Round final answers to 1 decimal place and intermediate z-value calculations to 2 decimal places.

Applicants must have a lower blood pressure limit of ------- and an upper blood pressure limit of

------- to qualify for the study.

3. Police Academy Acceptance Exams To qualify for a police academy, applicants are given a test of physical fitness. The scores are normally distributed with a mean of 67 and a standard deviation of 12. If only the top 17% of the applicants are selected, find the cutoff score. Round z-value calculations to 2 decimal places and the final answer up to the nearest whole number.

Cutoff score =

4.Life of Smoke DetectorsThe average lifetime of smoke detectors that a company manufactures is5years, or60months,and the standard deviation is9months.Find the probability that a random sample of31smoke detectors will have a mean lifetime between57and62months.Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answer to at least four decimal places and intermediatez-value calculations to two decimal places.

=P(57

5.The average number of moves a person makes in his or her lifetime is12and the standard deviation is3.5.Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answers to four decimal places and intermediatez value calculations to two decimal places.

Part 1 of 3 Find the probability that the mean of a sample of25people is less than10.

P (X < 10) =

Part 2: Find the probability that the mean of a sample of25people is greater than10.

=P(X>10) =

Part 3 of 3: Find the probability that the mean of a sample of25people is between11and12.

P (11 < X < 12) =

6. The average teacher's salary in a certain state is$37,764. Assume a normal distribution with= $5100. Assume that the sample is taken from a large population and the correction factor can be ignored. Use a TI-83 Plus/TI-84 Plus calculator and round the answers at least four decimal places.

(a) What is the probability that a randomly selected teacher's salary is greater than$39,500?

P(X>39,500) =

(b) For a sample of75teachers, what is the probability that the sample mean is greater than$38,700?

P(X>38,700) =

7.Cell Phone LifetimesA recent study of the lifetimes of cell phones found the average is24.1months. The standard deviation is3.4months. If a company provides its33employees with a cell phone, find the probability that the mean lifetime of these phones will be less than23.8months. Assume cell phone life is a normally distributed variable, the sample is taken from a large population, and the correction factor can be ignored. Use a TI-83 Plus/TI-84 Plus calculator. Round your answer to at least four decimal places.

P(X<23.8) =

8.Use the normal approximation to the binomial to find the probability forn=50,p0.8,andX=47.Roundz-value calculations to2decimal places and final answer to4decimalplaces.

The probability is=

9.Use the normal approximation to the binomial to find the probability forn=13,p0.5,andX8.Roundz-value calculations to2decimal places and final answer to4decimalplaces.

The probability is=

10.Use the normal approximation to the binomial to find the probability for=n=49,p0.7,andX40.Roundz-value calculations to2decimal places and final answer to at least4decimalplaces.

The probability is =

11. Single AmericansIn a recent year, about22%of Americans14years and older are single. What is the probability that in a random sample of230Americans14or older, more than33are single? Round the final answer to at least4decimal places and intermediatez-value calculations to2decimal places.

P(X>33) =

12.Mail OrderA mail order company has a7%success rate. If it mails advertisements to548people, find the probability of getting less than31sales. Roundz-value calculations to2decimal places and final answer to at least4decimal places.

P(X<31) =