Question

The amounts of electric bills for all households in a city have an approximately normal distribution with a mean of $110 and a standard deviation of $16. Let x be the mean amount of electric bills for a random sample of 16 households selected from the city.

(a) Compute the mean, of x

(b) Compute the standard deviation of x

(c) Comment on the shape of the sampling distribution of x

Answer 1

Solution :

Given that ,

mean =   = $110

standard deviation = = $16   

n = 16

mean of x = = 110

standard deviation of x= =  / n= 16 / 16=4