Question

The time it takes for climbers to reach the highest point of a mountain is normally distributed with a standard deviation of 0.75 hrs. If a sample of 35 people is drawn randomely from the population. what would be the standard error of the mean of the sample?

Answer 1

Hi, Elizah, and welcome to OpenStudy!

This kind of problem is very common in statistics. You are told that this or that (in this case, the time required to climb the mountain) is normally distributed, and you're given the standard deviation of this quantity. You take a sample from that population (in this case, a sample of n=35) and are asked to find the "standard error of the mean."

I'd strongly suggest that you look up that phrase, "standard error of the mean," since you'll be seeing this again and again and need to know its meaning and how to find it.

To help you get started, I did a quick Internet search for that term and came up with the following:

http://www.usablestats.com/lessons/sem

Note that the "standard error of the mean" is defined as\[\frac{ \sigma }{ \sqrt{n} },\] where that "sigma" represents the standard deviation of the population and n represents the number of samples taken.

Given that sigma =0.75 hour, and that n = 35, find the "standard error of the mean."

Please note that this is very often referred to as the "sample standard deviation."