Question

Suppose x has a distribution with μ = 69 and σ = 5.

(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 = 69 and σ_x = 5.No, the sample size is too small.     Yes, the x distribution is normal with mean μ_x = 69 and σ_x = 0.3.Yes, the x distribution is normal with mean μ_x = 69 and σ_x = 1.25.

(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 = 69 and σ_x = 5.No, the sample size is too small.     Yes, the x distribution is normal with mean μ_x = 69 and σ_x = 0.3.Yes, the x distribution is normal with mean μ_x = 69 and σ_x = 1.25.

Find P(65 ≤ x ≤ 70). (Round your answer to four decimal places.)

Answer 1

Solution:

a)

Yes, the x distribution is normal with mean μ_x = 69 and σ_x = 0.3.Yes, the x distribution is normal with mean μ_x = 69 and σ_x = 1.25.

b)

P( 65 70) = P((65 - 69) /1.25 <( - ) / (70 - 69) / 1.25))

= P(-3.2 Z 0.8)

= P(Z 0.8) - P(Z -3.2) Using standard normal table,  

= 0.7881 - 0.0007

= 0.7875

Probability = 0.7875