Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. the time it takes for climbers to reach the highest point of a mountain is normally distributed with a standard deviation of 0.75 hours. a sample of 35 people is drawn randomly from the population. the standard error of the mean of the sample is hours. (round off your answer to the nearest hundredth.)

Explanation:

Step1: Recall the formula for standard error of the mean

The formula for the standard error of the mean ($SE_{\bar{x}}$) is $SE_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard - deviation and $n$ is the sample size.

Step2: Identify the values of $\sigma$ and $n$

We are given that $\sigma = 0.75$ hours and $n = 35$.

Step3: Calculate the standard error of the mean

Substitute the values into the formula: $SE_{\bar{x}}=\frac{0.75}{\sqrt{35}}$.
First, calculate $\sqrt{35}\approx5.9161$. Then, $SE_{\bar{x}}=\frac{0.75}{5.9161}\approx0.13$.

Answer:

0.13