Question

6.5-4) Suppose x has a distribution with μ = 39 and σ = 20.

(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 = 39 and σ_x = 5.

No, the sample size is too small.   

Yes, the x distribution is normal with mean μ_x = 39 and σ_x = 1.3.

Yes, the x distribution is normal with mean μ_x = 39 and σ_x = 20

(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 = 39 and σ_x = 20.

No, the sample size is too small.

   Yes, the x distribution is normal with mean μ_x = 39 and σ_x = 5.

Yes, the x distribution is normal with mean μ_x = 39 and σ_x = 1.3.

b) Find P(35 ≤ x ≤ 40). (Round your answer to four decimal places.)_____________

Answer 1

Solution: Given that μ = 39 and σ = 20

(a) option A. Yes, the x distribution is normal with mean μx = 39 and σx = 5

(b) option C. Yes, the x distribution is normal with mean μx = 39 and σx = 5

P(35 ≤ x ≤ 40) = 0.3674