Question

The amounts of electricity bills for all households in a particular city have an approximately normal distribution with a mean of $145 and a standard deviation of $28. Let ū be the mean amount of electricity bills for a random sample of 20 households selected from this city. Find the mean and standard deviation of X. Round your answers to the nearest integer, if required. Mj = $ll Gü = $ Comment on the shape of the sampling distribution of t. The sampling distribution of is approximately normal A

Answer 1

Solution :

Given that ,

mean = $\mu$ = 145

standard deviation = $\sigma$ =28

n = 20

sample distribution of sample mean is ,

$\mu$$\bar x$ = $\mu$

$\mu$$\bar x$ = 145

sampling distribution of standard deviation

$\sigma$$\bar x$ =$\sigma$  / $\sqrt$ n = 28 / $\sqrt$ 20

$\sigma$$\bar x$ = 6.26=6 rounded

sampling distribution is approximately normal