Question

A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 24.6 pounds and a standard deviation of 8.0 pounds. If a sampling distribution is created using samples of the amounts of weight lost by 51 people on this diet, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.

Answer 1

Solution

Given, the Normal distribution with,

   = 24.6

= 8.0

n = 51 (sample size)

Let be the sample mean.we know that the sampling distribution of is normal with

Mean() = = 24.60

SD() = = 8.0/51​ = 1.120224 (It is called as the standard error of the mean)

Answer :The mean of the sampling distribution of sample means is 24.60