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QUESTION 3 Whenever the population has a normal probability distribution, the sampling distribution of X is a normal probability distribution for a. only large sample sizes b.only small sample sizes c. any sample size d. only samples of size thirty or greater Click Save and Submit to save and submit. Click Save All Answers to see all answers MacBook Air 90 14 FO FB A # 3 $ 4 % 5 & 7 2 6 8 9 T U

Answer 1

Let X be the population representing a normal population.

Then
X
= $\large \sum$ X_i / n is the linear combinationof X_i 's with coefficient vectors [ 1/ n , 1/ n , ,,,,,1/n]

We know since population characterized by random variable X follows normal so X_i follows normal distribution.

As X_i follows normal their linear combination will also follows normal distribution because of the property of linear distribution. Here
X
is linear the combination of X_i 's , hence  
X
follows normal distribution. It doesn't matter what is the sample size , as long as the statistic is the linear combination of X_i 's will follow automatically normal.

Ans : <c> any sample size.