Question

A random sample is drawn from a population with mean μ = 64 and standard deviation σ = 5.3. [You may find it useful to reference the z table.]

a. Is the sampling distribution of the sample mean with n = 17 and n = 34 normally distributed?

Yes, both the sample means will have a normal distribution.

No, both the sample means will not have a normal distribution.

No, only the sample mean with n = 17 will have a normal distribution.

No, only the sample mean with n = 34 will have a normal distribution.

b. Calculate the probability that the sample mean falls between 64 and 66 for n = 34. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Answer 1

Solution:-

a) No, only the sample mean with n = 34 will have a normal distribution.

For the normal distribution, we should have known population standard deviation and sample size should be greater than 30.

b) The probability that the sample mean falls between 64 and 66 for n = 34 is 0.4861.

x₁ = 64

x₂ = 66

By applying normal distruibution:-

z₁ = 0

z₂ = 2.2004

P( 0 < z < 2.2004) = P(z > 0) - P(z > 2.2004)

P( 0 < z < 2.2004) = 0.50 - 0.0139

P( 0 < z < 2.2004) = 0.4861