Question

Let x stand for the number of calories in each individual snack. 25 snacks are sampled at a time. The population mean is 95 calories and the population standard deviation is 2.5 calories. What is the mean and standard deviation of the sampling distribution of sample means?

a. mean = 19. standard deviation = 2.5
b. mean = 95, standard deviation = 0.5
c. mean = 95, standard deviation = 2.5
d. mean = 19. standard deviation = 0.5

Answer 1

b)

Mean of the sample μₓ = 95

Standard deviation of the sample (S) = 0.5

Explanation:

Step(i):-

Given sample size 'n' = 25

Mean of the Population μ = 95 calories

Standard deviation of the Population = 2.5 calories

Step(ii):-

Mean of the sample μₓ = μ

Mean of the sample μₓ = 95

Standard deviation of the sample

`= (S.D)/(√(n) ) = (2.5)/(√(25) ) =0.5`