Question

Suppose x has a normal distribution with mean μ = 57 and standard deviation σ = 12.

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

μx	=
σx	=

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

μx	=
σx	=

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

μx	=
σx	=

How do the x distributions compare for the various samples sizes?

a. The means are the same, but the standard deviations are increasing with increasing sample size.

b. The means and standard deviations are the same regardless of sample size.    

c. The standard deviations are the same, but the means are increasing with increasing sample size.

d. The means are the same, but the standard deviations are decreasing with increasing sample size.The standard deviations are the same, but the means are decreasing with increasing sample size.

Answer 1

Solution

Suppose x has a normal distribution with mean μ = 57 and standard deviation σ = 12.

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

(a)

For Sample Size = n = 4, The Distribution of is Normal Distribution with mean = mean of the population = 52 and Standard Deviation =

Thus,

for n = 4,

(b)

For Sample Size = n = 16, The Distribution of is Normal Distribution with = mean of the population = 52 and Standard Deviation =

Thus,

for n = 16,

(c)

For Sample Size = n = 100, The Distribution of is Normal Distribution with mean = = mean of the population = 52 and Standard Deviation = \sigma

Thus,

for n = 100

(d) Correct option:

The means are the same, but the standard deviations are decreasing with increasing sample size.