Question

For samples of the specified size from the population described, find the mean and standard deviation of the sample mean . The population mean and the population standard deviation of the sampled population are, respectively, 55.7 and 3.8. n=256

(A) μ = 3.8; σ = 0.2
(B) μ= 14.1; σ = 1.1
(C) μ = 0.2; σ = 55.7
(D) μ = 55.7; σ = 3,8(E) μ = 55.7; σ = 0.2375.

Answer 1

mean of sample is 55.7

sample standard deviation is 0.2375

Explanation:

given data

population mean = 55.7

population standard deviation = 3.8

n = 256

to find out

the mean and standard deviation

solution

we know directly mean of sample is mean of population

i.e. mean of sample = 55.7

and standard deviation will be calculate by this formula

sample standard deviation = population standard deviation /
`√(n)`

sample standard deviation = 3.8 /
`√(256)`

sample standard deviation = 3.8/ 16

sample standard deviation = 0.2375

so last option is right

(E) μ = 55.7 , σ = 0.2375.