Suppose x has a distribution with 26 and 16 a If random sa

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.)

Solution

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