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Q2: According to a survey by the Administrative Management Society, one-half of U.S. companies give employees 4 weeks of vacation after they have been with the company for 15 years. Find the probability that among 6 companies surveyed at random, the number that give employees 4 weeks of vacation after 15 years of employment is (a) anywhere from 2 to 5; (b) fewer than 3.

Carry your intermediate computations to at least four decimal places, and round your answer to at least two decimal places.

Provide a 90% confidence interval estimate of the population variance (to 1 decimal).

Table

Season no of days Daily demand Avarage cost per occupied room per day

Peak Season 210 700 100

Noram Season 130 600 85

Slack Season 90 500 65

An Italian Ice (snowcone) retailer is examining his profits for the spring season of the previous year. He realizes that his sales are based on the daily weather: sunny, average, or cold. He estimates that this year the probability of it being sunny is 0.2, average 0.5, and cold 0.3. His gross sales on these three types of days average $50, $35, and $10 respectively.

a. Find the expected income in any one day.

b. If the average supplies cost $18, what is the expected daily profit?

Age group Never Former Current

10-15 35 62 95

16-20 120 73 107

20-25 90 60 63

26-30 109 77 134

30-35 82 52 140

36-40 40 115 103

Above 40 68 82 158

Using the above data can we conclude that there is a difference among population residual means at 5% level of significance in terms of smoking history?

(i) Draw a tree diagram to illustrate the above event.

(ii) Calculate the probability that at least one person passes the test.