Question

The living spaces of all homes in a city have a mean of 2300 square feet and a standard deviation of 500 square feet. Let x be the mean living space for a random sample of 25 homes selected from this city.

Find the mean and standard deviation of the sampling distribution of x.

Answer 1

the mean and standard deviation is 2300 and 100 respectively

Explanation:

Given that

Mean = 2300

Standard deviation = 500

let us assume the x be the mean of living space

And, the sample is of 25 homes

We need to find out the mean and the standard deviation

So here mean = 2300

And, the standard deviation

= 500 ÷√25

= 500 ÷ 5

= 100

hence, the mean and standard deviation is 2300 and 100 respectively