Question

Suppose x has a normal distribution with mean μ = 55 and standard deviation σ = 7.

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?

The means are the same, but the standard deviations are increasing with increasing sample size.The means and standard deviations are the same regardless of sample size.    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.The standard deviations are the same, but the means are increasing with increasing sample size.

Answer 1

Solution :

Given that ,

mean = = 55

standard deviation = = 7

(a)n = 4

sampling distribution of sample mean = = 55

sampling distribution of standard deviation = =  / n= 7 / 4=3.5

(b)

n = 16

sampling distribution of sample mean = = 55

sampling distribution of standard deviation = =  / n= 7 / 16=1.75

(c)

n = 100

sampling distribution of sample mean = = 55

sampling distribution of standard deviation = =  / n= 7 / 100=0.70