Question

A random sample is selected from a population with mean μ = 98 and standard deviation σ = 10. Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes. (Round the answers to three decimal places.)

(a) n = 8
μ =
σ =

(b) n = 18
μ =
σ =

(c) n = 38
μ =
σ =

(d) n = 55
μ =
σ =

(f) n = 110
μ =
σ =

(e) n = 440
μ =
σ =

Answer 1

Solution :

Given that,

mean = = 98

standard deviation = = 10

(a)

n = 8

= 98

= / n = 10 / 8 = 3.536

(b)

n = 18

= 98

= / n = 10 / 18 = 2.357

(c)

n = 38

= 98

= / n = 10 / 38 = 1.622

(d)

n = 55

= 98

= / n = 10 / 55 = 1.348

(f)

n = 110

= 98

= / n = 10 / 110 = 0.953

(e)

n = 440

= 98

= / n = 10 / 440 = 0.477