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

Answer:

0.9192 or 91.92%

Step-by-step explanation:

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

$z=\frac{X-\mu}{s}$

And,

$s=\frac{\sigma}{\sqrt{n}}$

Where:

X = 109.8 inches

μ = mean = 107 inches

σ = standard derivation = 12

n = 36

Then,

$\begin{gathered} s=\frac{12}{\sqrt[]{36}} \\ s=\frac{12}{6} \\ s=2 \end{gathered}$

And,

$\begin{gathered} z=\frac{X-\mu}{s} \\ z=\frac{109.8-107}{2} \\ z=\frac{2.8}{2} \\ z=1.4 \end{gathered}$

Finally, we can