Question

Solve the problem. Use the Central Limit Theorem. (7) 6) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 109 inches, and a standard deviation of 10 inches. What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 111.8 inches

Answer 1

Answer:

The answer is "0.9192".

Step-by-step explanation:  

$\mu=109\\\\\sigma=10\\\\n=25\\\\\to P(\bar{x}< 111.8)=P(\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} < \frac{111.8-109}{\frac{10}{\sqrt{25}}})$

                          $=P(2$