Solve the problem.
-The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 74 inches, and a standard deviation of 12 inches. What is the probability that the mean annual snowfall during 36 randomly picked years will exceed 76.8 inches?
A)0.0026
B)0.5808
C)0.4192
D)0.0808

Question

Quizplus · Accepted Answer

To find the probability that the mean annual snowfall during 36 randomly picked years will exceed 76.8 inches, we use the formula for the standard error of the mean: $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the standard deviation and $n$ is the sample size. Here, $\sigma = 12$ inches and $n = 36$, so $\sigma_{\bar{x}} = \frac{12}{\sqrt{36}} = 2$ inches. We then calculate the z-score for 76.8 inches: $z = \frac{76.8 - 74}{2} = 1.4$. Looking up 1.4 on the z-table gives us the probability of 0.9192 for being below 76.8 inches. Therefore, the probability of exceeding 76.8 inches is $1 - 0.9192 = 0.0808$.

Solve the Problem. -The Amount of Snowfall Falling in a Certain Mountain Range