Question

Suppose x has a distribution with μ = 40 and σ = 15.

(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 = 40 and σ_x = 15.Yes, the x distribution is normal with mean μ_x = 40 and σ_x = 0.9.    Yes, the x distribution is normal with mean μ_x = 40 and σ_x = 3.75.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 = 40 and σ_x = 3.75.    Yes, the x distribution is normal with mean μ_x = 40 and σ_x = 15.Yes, the x distribution is normal with mean μ_x = 40 and σ_x = 0.9.

The bold question needs solving.
Find P(36 ≤ x ≤ 41). (Round your answer to four decimal places.)
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Answer 1

Solution :

Given that,

mean = = 40

standard deviation = = 15

n = 16

a) No, the sample size is too small

b) = = 40

= / n = 15 / 16 = 3.75

Yes, the x distribution is normal with mean μx = 40 and σx = 3.75.

P(36 41 )  

= P[(36 - 40) / 3.75 ( - ) / (41 - 40) / 3.75 )]

= P(-1.07 Z 0.27)

= P(Z 0.27) - P(Z -1.07)

Using z table,  

= 0.6064 - 0.1423  

= 0.4641