Question

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 meanannual precipitation during 36 randomly picked years will be lessthan 109.8 inches?

Answer 1

0.9192 or 91.92%

Step-by-step explanation:

First, we have to find the z score, using the formula above:

`z=(X-\mu)/(s)`

And,

`s=(\sigma)/(√(n))`

Where:

X = 109.8 inches

μ = mean = 107 inches

σ = standard derivation = 12

n = 36

Then,

`\begin{gathered} s=\frac{12}{\sqrt[]{36}} \\ s=(12)/(6) \\ s=2 \end{gathered}`

And,

`\begin{gathered} z=(X-\mu)/(s) \\ z=(109.8-107)/(2) \\ z=(2.8)/(2) \\ z=1.4 \end{gathered}`

Finally, we can