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

The answer is "0.9192".

Explanation:

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

`=P(2<1.4)\\\\=\phi (1.4)\\\\=0.9192`