Question

Suppose x has a distribution with μ = 45 and σ = 13.

(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 = 45 and σ x = 13.

Yes, the x distribution is normal with mean μ x = 45 and σ x = 3.25.

Yes, the x distribution is normal with mean μ x = 45 and σ x = 0.8.

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?

No, the sample size is too small.

Yes, the x distribution is normal with mean μ x = 45 and σ x = 0.8.

Yes, the x distribution is normal with mean μ x = 45 and σ x = 3.25.

Yes, the x distribution is normal with mean μ x = 45 and σ x = 13.

(c) Find P(41 ≤ x ≤ 46). (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

mean = = 45

standard deviation = = 13

n = 16

a) No, the sample size is too small.

b) = = 45

= / n = 13 / 16 = 3.25

Yes, the x distribution is normal with mean μ x = 45 and σ x = 3.25

c) P(41 46)  

= P[(41 - 45) / 3.25 ( - ) / (46 - 45) / 3.25 )]

= P(-1.23 Z 0.31)

= P(Z 0.31) - P(Z -1.23)

Using z table,  

= 0.6217 - 0.1093

= 0.5124