Answer the following Question :

1. Based on historical data, sales for a particular cosmetic line follow a continuous uniform distribution with a lower limit of $2,500 and an upper limit of $5,000.

A. What are the mean and standard deviation of this uniform distribution?

B. What is the probability that sales exceed $4,000?

2. Many people apply for jobs to serve as paramedics or firefighters, yet they cannot complete basic physical fitness standards. A study found that 77% of all candidates for paramedic and firefighter positions were overweight or obese.

A. What is the expected value and the standard error of the sample proportion derived from a random sample of 100 candidates for paramedic or firefighter positions?

b. What are the expected value and the standard error of the sample proportion derived from a random sample of 200 candidates for paramedic or firefighter positions?

3.The scheduled arrival time for a daily flight from Boston to New York is 9:25 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:15 am and a late arrival time of 9:55 am.

a. Calculate the mean and the standard deviation of the distribution.

b. What is the probability that a flight arrives late (later than 9:25 am)?

c. Vee Products Company is investigating the possibility of producing and marketing backyard storage sheds.

d. Undertaking this project would require the construction of either a large or a small manufacturing plant. Vee, of course, has the option of not developing the new product line at all.

e. The market for the product produced-storage sheds-could be either favorable or unfavorable. Probability - 0.6 favorable and 0.40 unfavorable market.

f. A.Construct a Decision tree,

g. B.Construct a Decision Table showing market for product produced,

h. C.Calculate Maximax, Maximin and equally likely,

i. D.Construct a Decision Table under uncertainty,

j. E.Determine the expected monetary value (EMV) for each alternative.

4.The mean height of adult men in the u.s is 69.7 inches, with a standard deviation of 3 inches.

(a)A sociologist believes that taller men may be more likely to be promoted to position of leadership, so the mean height µ of male business executives may be greater than the mean height of the entire male population.

(b)A simple random of 100 male business executives has a mean height of 69.9in. Assume that the standard deviation of male executive heights is α=3 inches . Can we conclude that the male business executives are taller on average than the general male population at the α= 0.05 level

5.Scientists want to estimate the mean weight of mice after they have been fed a special diet. From previous studies, it is known that the weight is normally distributed with standard deviation 3 grams. How many mice must be weighed so that a 95% confidence interval will have a margin of error of 0.5 grams?