Question

In: Statistics and Probability

Solve the problem. The annual precipitation amounts in a certain mountain range are normally distributed with...

Solve the problem. The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 107 inches, and a standard deviation of 12 inches. What is the probability that the mean annual precipitation during 36 randomly picked years will be less than 109.8 inches?

A. 0.9192

B. 0.4192

C. 0.5808

D. 0.0808

Solutions

Expert Solution

Solution :

Given that ,

mean = = 107

standard deviation = = 12

n = 36

= 107 and

= / n = 12 / 36 = 12 / 6 = 2

P( < 109.8) = P(( - ) / < (109.8 - 107) / 2) = P(z < 1.4)

Using standard normal table,

P( < 109.8) = 0.9192

Probability = 0.9192

Option A) is correct .

orchestra answered 1 year ago
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