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
[tex]\mu=310.4\text{ million gallons per day}[/tex]
Standard deviation : [tex]\sigma=40 \text{ million gallons per day}[/tex]
Let x be the combined storage capacity requires by the reservoir on a random day.
Z-score : [tex]\dfrac{x-\mu}{\sigma}[/tex]
[tex]z=\dfrac{350-310.4}{40}=0.99[/tex]
The probability that a day requires more water than is stored in city reservoirs is :
[tex]P(x>350)=P(z>0.99)=1-P(z<0.99)\\\\=1-0.8389129=0.1610871\approx0.161[/tex]
Hence, the probability that a day requires more water than is stored in city reservoirs is 0.161
