Statistics Homework

1. Let Z be standard normal random variable. Calculate the following probabilities, round your responses to at least three decimals

a. P (Z > -1.97) =

b. P (Z ≤-1.71) =

c. P (1.01 < Z < 2.20) =

2. Let Z be a standard normal random variable. Determine the value of c.

a. P (-c≤ Z ≤ c) 0.9700

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

3. Let Z be standard normal random variable; determine c.

P (c ≤ Z ≤ -1.22) = 0.0745

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

4. Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 12 million dollars and a standard of deviation of 1.3 million dollars. One health care information systems company considers a quarter a “failure” if it is sales level that quarter is in the bottom 10% of all quarterly sales levels. Determine the sales level (in millions of dollars) that is the cutoff between quarters that are considered “failures” by that company and quarters that are not. Carry your intermediate computations to at least four decimals places. Round your answers to one decimals place

5. A psychologist has designed a questionnaire to measure individuals’ aggressiveness. Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80. Suppose also that exactly 5% of the scores exceed 800. Find the mean of the distribution of scores. Carry your intermediate computations to at least four decimals places. Round your answer to at least one decimal place.

6. 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 of 560 and a standard deviation of 125. The individuals who exceed 700 on this test are potential leaders. What proportion of the population are potential leaders? Round your answer to at least four decimals places

7. A multiple -choice examination consists of 80 questions, each having possible choices, a, b, c, d, and e. Approximate the probability that a student will get at least 13 answers correct if she randomly guesses at each answer. (note that, if she randomly guesses at each answer, then the probability that she gets any one answer correct is 0.2) 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

8. A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 16. A randomly selection group of 40 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 114.2. If the organization’s claim is correct, what is the probability of having a sample mean of 114.2 or less for a random sample of this size? Carry your intermediate computations to at least four decimals places. Round your answer to at least three decimal places.

9. Empirical research on stock market data for two consecutive trading days indicates that 60% of the stocks that went up on the first day also went up on the second day. Yesterday 600 stocks went up.

a. Find the mean P, when p gives the proportion of the 600 stocks that went up yesterday that will go up today

b. Fin the standard deviation of p.

c. Compute an approximation for P (p > 0.58, which is the probability that more than 58% if the stocks that went up yesterday will go up again today.

a. Find the mean of p, where p gives the proportion of the ,600, stocks that went up yesterday that will go up today.

b. Find the standard deviation of, p, Compute an approximation for P>p0. 58, which is the probability that more than ;58%m of the stocks that went up yesterday will go up again today. Round your answer to four decimal places.

In problem # 9. I was trying to put upside down less than signal above the P