Question

If a population is known to be normally distributed with size 25 selected from the population? 89 and 15, what will be the characteristics of the sampling distribution for x based on a random sample of - 89 (Type an integer or a decimal.) - 3 (Type an integer or a decimal.) Describe the sampling distribution of the sample. Choose the correct answer below O O A. The sampling distribution is skewed right because the population is normally distributed and the sample size is less than 30 B. The sampling distribution is normally distributed by the Central Limit Theorem. C. The sampling distribution is normally distributed because the population is normally distributed O 0. The sampling distribution is skewed left because the population is normally distributed and the sample size is less than 30 O E. The sampling distribution cannot be described without actual data.

Answer 1

since X $\sim$ N(89 , 152)  

X $\sim$ N(89 , 225)

n = 25

Since population standard deviation is known then by central limit theorm sample mean will follow normal distribution with mean  $\mu$ and variance $\sigma ^{2}/n$

$\bar{X}$$\sim$ N( $\mu$ ,  $\sigma ^{2}/n$ )

$\bar{X}$$\sim$ N(89 , 225/25)

$\bar{X}$$\sim$ N(89 , 9)

Sampling distribution is normally distributed by central limit theorem