1) Sound City sells the ClearTone-400 satellite car radio. For this radio, historical sales records over the last 100 weeks show 3 weeks with no radios sold, 25 weeks with one radio sold, 30 weeks with two radios sold, 30 weeks with three radios sold, 7 weeks with four radios sold, and 5 weeks with five radios sold. Calculate _x, _x², and _x, ofx,the number of ClearTone-400 radios sold at Sound City during a week using the estimated probability distribution.(Round your answers to 2 decimal places.)

2) In order to gain additional information about respondents, some marketing researchers have used ultraviolet ink to precode questionnaires that promise confidentiality to respondents. Of 168 randomly selected marketing researchers who participated in an actual survey, 122 said that they disapprove of this practice. Suppose that, before the survey was taken, a marketing manager claimed that at least 84 percent of all marketing researchers would disapprove of the practice.

(a)Assuming that the manager's claim is correct, calculate the probability that 122 or fewer of 168 randomly selected marketing researchers would disapprove of the practice. Use the normal approximation to the binomial.(Round z value to 2 decimal places. Round your answer to 5 decimal places.)

3) The scores on the entrance exam at a well-known, exclusive law school are normally distributed with a mean score of 188 and a standard deviation equal to 86. At what value should the lowest passing score be set if the school wishes only 2.5 percent of those taking the test to pass?(Round your answer to nearest whole number.) set lowest passing score to?

4) Congratulations! You have just won the question-and-answer portion of a popular game show and will now be given an opportunity to select a grand prize. The game show host shows you a large revolving drum containing four identical white envelopes that have been thoroughly mixed in the drum. Each of the envelopes contains one of four checks made out for grand prizes of 21, 41, 61, and 81 thousand dollars. Usually, a contestant reaches into the drum, selects an envelope, and receives the grand prize in the envelope. Tonight, however, is a special night. You will be given the choice of either selecting one envelope or selecting two envelopes and receiving the average of the grand prizes in the two envelopes. If you select one envelope, the probability is 1/4 that you will receive any one of the individual grand prizes 21, 41, 61, and 81 thousand dollars.

Assume you select two envelopes. There are six combinations, or samples, of two grand prizes that can be randomly selected from the four grand prizes 21, 41, 61, and 81 thousand dollars. The six samples are (21, 41), (21, 61), (21, 81), (41, 61), (41, 81), and (61, 81). What is the probability that you will receive a sample mean grand prize of at least 51 thousand dollars?(Enter the reduced fraction.)

5) Congratulations! You have just won the question-and-answer portion of a popular game show and will now be given an opportunity to select a grand prize. The game show host shows you a large revolving drum containing four identical white envelopes that have been thoroughly mixed in the drum. Each of the envelopes contains one of four checks made out for grand prizes of 20, 40, 60, and 80 thousand dollars. Usually, a contestant reaches into the drum, selects an envelope, and receives the grand prize in the envelope. Tonight, however, is a special night. You will be given the choice of either selecting one envelope or selecting 2 envelopes and receiving the average of the grand prizes in the two envelopes. If you select one envelope, the probability is 1/4 that you will receive any one of the individual grand prizes 20, 40, 60, and 80 thousand dollars.

Assume you select two envelopes. There are six combinations, or samples, of two grand prizes that can be randomly selected from the four grand prizes 20, 40, 60, and 80 thousand dollars. Four of these samples are (40, 60), (20, 40), (60, 80), and (40, 80). Select the other two samples.

• (20, 40) & (60, 80)
• (60, 80) & (40, 80)
• (20, 80) & (20, 60)
• (40, 60) & (20, 40)

6) In an article in theJournal of Management,Joseph Martocchio studied and estimated the costs of employee absences. Based on a sample of 176 blue-collar workers, Martocchio estimated that the mean amount ofpaidtime lost during a three-month period was 1.3 days per employee with a standard deviation of 1.2 days. Martocchio also estimated that the mean amount ofunpaidtime lost during athree-monthperiod was 1.3 day per employee with a standard deviation of 1.4 days.

Suppose we randomly select a sample of 100 blue-collar workers. Based on Martocchio's estimates:

(a)What is the probability that the average amount ofpaidtime lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days?(Use the rounded mean and standard error to compute the rounded Z-score used to find the probability. Round means to 1 decimal place, standard deviations to 2 decimal places, and probabilities to 4 decimal places. Round z-value to 2 decimal places.)

(b)What is the probability that the average amount ofunpaidtime lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days?(Use the rounded mean and standard error to compute the rounded Z-score used to find the probability. Round standard deviations to 2 decimal places andprobabilities to 4 decimal places. Round z-value to 2 decimal places.)

(c)Suppose we randomly select a sample of 100 blue-collar workers, and suppose the sample mean amount of unpaid time lost during a three-month period actually exceeds 1.5 days. Would it be reasonable to conclude that the mean amount of unpaid time lost has increased above the previously estimated 1.3 days?

7) Suppose that we will randomly select a sample ofn= 84 elements from a population and that we will compute the sample proportion

of these elements that fall into a category of interest. If the true population proportionpequals .9:

(a)Describe the shape of the sampling distribution ofp^. Why can we validly describe the shape

(b)Find the mean and the standard deviation of the sampling distribution of

.(Round the answers to 2 decimal places.)