Answer to Question #153215 in Statistics and Probability for tolga

Question

1.The amount of water consumed by a person per day on the job is normally distributed with mean 2 lts. and standard deviation 0.5 lt. A company supplies its employees with 200 lts of water daily. The company has 100 employees.

a. Find the probability that the water supplied by the company will not satisfy the water demanded by its employees.

b. Find the probability that in the next 4 days the company will not satisfy the water demanded by its employees on at least 1 of these 4 days. Assume that the amount of water consumed by the employees of the company is independent from day to day. 

Answer 1

a) P($\overline{X}>2) = P(x>z) = P(x>\frac{2-2}{0.5/\sqrt{100}}) = P(x>0) = 0.5$

b) A - in the next 4 days the company will not satisfy the water demanded by its employees on at least 1 of these 4 days

P(A) = 1 - (P($\overline{X}<2)$)⁴ = 1 - 0.5⁴ = 0.9375