Suppose x has a distribution with = 26 and = 16. (a) If random samples of size n

Question

Suppose x has a distribution with = 26 and = 16.

(a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?

A Yes, the x distribution is normal with mean x = 26 and x = 1.0.

B No, the sample size is too small.    

C Yes, the x distribution is normal with mean x = 26 and x = 16.

D Yes, the x distribution is normal with mean x = 26 and x = 4.

(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?

A Yes, the x distribution is normal with mean x = 26 and x = 4

B .No, the sample size is too small.    

C Yes, the x distribution is normal with mean x = 26 and x = 16.

D Yes, the x distribution is normal with mean x = 26 and x = 1.0.

(c) Find P(22 x 27). (Round your answer to four decimal places.)

Explanation / Answer

According to the Central Limit Theorem the mean of the sample means equals
the population mean which is 26, and the standard deviation of the sample
means is 16/sqrt16) = 4 .
a)
D Yes, the x distribution is normal with mean x = 26 and x = 4.
b)
A Yes, the x distribution is normal with mean x = 26 and x = 4
c)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 22) = (22-26)/16
= -4/16 = -0.25
= P ( Z <-0.25) From Standard Normal Table
= 0.40129
P(X < 27) = (27-26)/16
= 1/16 = 0.0625
= P ( Z <0.0625) From Standard Normal Table
= 0.52492
P(22 < X < 27) = 0.52492-0.40129 = 0.1236                  

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