Question

g Water use in the summer is normally distributed with a mean of 310.4 million gallons per day and a standard deviation of 40 million gallons per day. City reservoirs have a combined storage capacity of 350 million gallons. The probability that a day requires more water than is stored in city reservoirs is P(X > 350)= 1 - P (Z < b). What is the value of b? Please report your answer in 3 decimal places.

Answer 1

Answer: The value of b = 0.99

The probability that a day requires more water than is stored in city reservoirs is 0.161.

Step-by-step explanation:

Given : Water use in the summer is normally distributed with

$\mu=310.4\text{ million gallons per day}$

Standard deviation : $\sigma=40 \text{ million gallons per day}$

Let x be the combined storage capacity requires by the reservoir on a random day.

Z-score : $\dfrac{x-\mu}{\sigma}$

$z=\dfrac{350-310.4}{40}=0.99$

The probability that a day requires more water than is stored in city reservoirs is  :

$P(x>350)=P(z>0.99)=1-P(z$    

Hence, the probability that a day requires more water than is stored in city reservoirs is 0.161