Question

Suppose x has a normal distribution with mean μ = 45 and standard deviation σ = 10.

Describe the distribution of x values for sample size n = 4. (Round σx to two decimal places.)

μx =

σx =

Describe the distribution of x values for sample size n = 16. (Round σx to two decimal places.)

μx =

σx =

Describe the distribution of x values for sample size n = 100. (Round σx to two decimal places.)

μx =

σx =

Answer 1

Solution:

We are given that the random variable x has normal distribution.

µ = 45

σ = 10

Describe the distribution of x values for sample size n = 4.

WE know that the estimate for the mean of the sampling distribution of sample mean is the population mean. The estimate for the standard deviation of the sampling distribution of the sample mean is the standard error σ/sqrt(n).

We have

n = 4

μ_x̄ = µ = 45

σ_x̄ = σ/sqrt(n) = 10/sqrt(4) = 5

σ_x̄ = 5.00

Describe the distribution of x values for sample size n = 16.

We have

n = 16

μ_x̄ = µ = 45

σ_x̄ = σ/sqrt(n) = 10/sqrt(16) = 10/4 = 2.50

σ_x̄ = 2.50

Describe the distribution of x values for sample size n = 100

We have

n = 100

μ_x̄ = µ = 45

σ_x̄ = σ/sqrt(n) = 10/sqrt(100) = 10/10 = 1.00

σ_x̄ = 1.00