Probability and Statistics (Answer up to 7th decimal point**)

And please give the answer step-by-step as I want to know how to calculate the answer, thanks.

Q5. (12%) The editor of a book publishing company decides whether to publish a textbook. Before reaching a publishing decision, the book will be reviewed for a positive or negative feedback. In the past, 99% of the huge successes received positive feedbacks, 70% of the moderate successes received positive feedbacks, 40% of the breakeven received positive feedbacks, and 20% of the losers received positive feedbacks. Based on the books published by the company, x% of them are huge successes, 20% of them are moderate successes, y% are breakeven, and 25% are losers.

(a) Given that the probability of a book that receives a positive feedback is 0.469, find x% and y%.

(b) Based on (a), if the book receives a positive feedback, what is the probability that it will be a huge success or a moderate success?

(c) Learning from the past experience, the editor sets up a new rule. For each book that receives negative feedback, there is no chance that the editor will publish it. On the other hand, for each book that receives a positive feedback, there is 80% chance that the editor will publish it. The editor receives 12 reviews and he makes the decision based on each feedback separately. Given that no more than 6 books will be published, what is the probability that no less than 3 books will be published?

Q6. (20%)

(a) In property management of shopping malls, a shopping mall is said to have a satisfactory customer service if the mean score of its customer service is greater than 85. The property management manager of a shopping mall claims that his mall is about to obtain a satisfactory customer service. Fifty customers are randomly selected to evaluate the customer service of the mall, their scores have a mean of 86 and a standard deviation of 14. Assume that the score of the customer service is normally distributed. Is there enough evidence to support the claim of the property management manager at 1% level of significance?

(b) The Human Resources Manager of an international company would like to compare the weekly working hours per person between employees in City A and City B. Random samples are drawn and the results are summarized below:

City A - Sample size: 15, Mean (hours): 42, Standard deviation (hours): 2.8

City B - Sample size: 16, Mean (hours): 44, Standard deviation (hours): 3.0

Can we conclude that the true mean weekly working hours per person between employees in City A and City B are different at 10% level of significance? Justify your assumptions.

Q7. (16%) A study was conducted to find out how certain disease may affect the blood pressures of patients in various age groups. Randomly selected samples of 80 patients with the disease were divided into three age groups, and their systolic blood pressures (measured in mmHg) were recorded. Below are the statistics.

Sample 1 (less than 25 years old) - n: a, : 3300, s: 10

Sample 2 (between 25 and 55) - n: b, : 3976, s: 8.5

Sample 3 (over 55) - n: 22, : 3256, s: 9

Assume the systolic pressures of patients in each of the three age groups were normally distributed and that the three groups had roughly the same variance in systolic blood pressures. Given that the sum of squares for errors is 6551.75. Perform ANOVA to determine if there are significant differences among the average systolic blood pressures of the individuals in these three groups at =0.05.