Suppose you had a population of fish whose lengths were norm

Suppose you had a population of fish whose lengths were normally distributed with a mean of 50 centimeters and a standard deviation of 5 centimeters. You draw a simple random sample of size 10, record the length of each fish, and calculate the mean of the sample lengths. What do you think your sample mean would most likely be? Explain your answer using what you know about random samples and sample means.

Solution

sample mean of a random sample taken from normally distributed population follows normal distribution with mean equals to population mean and variance equal to (population variance/ sample size)

So, sample mean is normally distributed with mean = 50.

And in a normal distribution peak lies at mean.

So, sample mean most likely would be 50