Question

Suppose x has a distribution with μ = 28 and σ = 17.

(a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?

Yes, the x distribution is normal with mean μ_x = 28 and σ_x = 4.25.Yes, the x distribution is normal with mean μ_x = 28 and σ_x = 1.1.    Yes, the x distribution is normal with mean μ_x = 28 and σ_x = 17.No, the sample size is too small.

(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?

Yes, the x distribution is normal with mean μ_x = 28 and σ_x = 4.25.Yes, the x distribution is normal with mean μ_x = 28 and σ_x = 1.1.    No, the sample size is too small.Yes, the x distribution is normal with mean μ_x = 28 and σ_x = 17.

Find P(24 ≤ x ≤ 29). (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

mean = = 28

standard deviation = = 17

n = 16

= = 28

= / n = 17 / 16 = 4.25

a) Yes, the x distribution is normal with mean μ_x = 28 and σ_x = 4.25.

b) No, the sample size is too small

P( 24 29)  

= P[(24 - 28) /4.25 ( - ) / (29 - 28) / 4.25)]

= P(-0.94 Z 0.24)

= P(Z 0.24) - P(Z -0.94)

Using z table,  

= 0.5948 - 0.1736

= 0.4212