The amount of mineral water consumed by a person per day on the job is normally

Question

The amount of mineral water consumed by a person per day on the job is normally distributed with mean 19 ounces and standard deviation 5 ounces. A company supplies its employees with 2000 ounces of mineral water daily. The company has 100 employees. a. Find the probability that the mineral water supplied by the company will not satisfy the water demand 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 mineral water consumed by the employees of the company is independent from day to day. c. Find the probability that during the next year (365 days) the company will not satisfy the water demanded by its employees on more than 15 days.

Explanation / Answer

Solution:

a) Given that = 19 and = 5, n = 100 E(T0) = (19)(100) = 1900
T0 ~ N( = 19, = 5) sd(T0) = (5) 100 = 50

P(T0 >2000) = P(Z > 2000-1900/50) = P(X >2) = 1-P(Z 2)
= 1- 0.9772
= 0.0228

b) Y~bin(n=4, P = 0.0228)
P(Y 1) = 1-P(Y < 1)
= 1-P(Y = 0)
= 1-4C0 (0.0228)^0 (0.9772)^4 = 0.0881

c) np = = 8.322 > 5 & nq = 356.678 >5
npq = 8.1323
npq = = 2.8517   
P(X 15) = 1-P(X 15)
= 1-P(Z 15.5-8.322/2.8517)
= 1-P(Z 2.517)
= 1-0.9941 = 0.0059

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