1. Leo is a very active dog that requires long walks at least 3 times a day. Assume that the following is the distribution of the number of times Leo goes for long walks.

x	3	4	5
p(x)	0.1	0.6	0.3

Assume that the number of times Leo goes for long walks is independent from day to day.

A. Find the sampling distribution of the mean number of times Leo goes for walks of two randomly selected days. That is, n=2. Hint: Let ₁, ₂ be the number of times Leo goes for walks in the first and second randomly selected days. You are asked to determine the sampling distribution of X=2x1+x2.

B. What is the sampling distribution of the mean of 40 randomly selected days (n=40)?

C. What the probability that the average of 40 randomly selected days is more than 4.1?

2. A vaccine is found to be 85% effective in preventing a certain disease. The vaccine is given to 40 people.

A. Approximate the probability that the vaccine is effective for no more than 30 of the people who received it?

B. Approximate the probability that the vaccine will be effective for at least 32 and at most 38 people who received it?