Question

15. The amount of rainfall in a certain place is a normal random variable with a mean of 28, and a standard deviation of 5. The probability that the amount of rain will exceed the capacity of the local reservoir is 0.10. What is the capacity of the reservoir? (a) 34.4 (b) 37.5 (c) 40.6 (d) 44.2 (e) 48.3

Answer 1

Solution :

Using standard normal table,

P(Z > z) = 0.10

1 - P(Z < z) = 0.10

P(Z < z) = 1 - 0.10

P(Z < 1.28) = 0.9

z = 1.28

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.28 * 5 + 28 = 34.4

The capacity of the resevoir is 34.4

option (a)