Question

33) Suppose x has a distribution with μ = 84 and σ = 9. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 84 and σ x = 2.25. Yes, the x distribution is normal with mean μ x = 84 and σ x = 0.6. Yes, the x distribution is normal with mean μ x = 84 and σ x = 9. (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 = 84 and σ x = 9. Yes, the x distribution is normal with mean μ x = 84 and σ x = 2.25. No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 84 and σ x = 0.6. Find P(80 ≤ x ≤ 85). (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

mean = = 84

standard deviation = = 9

n = 16

a) No, the sample size is too small.

b) Yes, the x distribution is normal with mean μ x = 84 and σ x = 2.25

=   = 84

= / n = 9 / 16 = 2.25

P(80 85)  

= P[(80 - 84) / 2.25 ( - ) / (85 - 84) / 2.25)]

= P(-1.78 Z 0.44)

= P(Z 0.44) - P(Z -1.78)

Using z table,  

= 0.6700 - 0.0375   

= 0.6325