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Suppose individual X scores in the population follow a normal distribution N(38, 20). A researcher draws...

Suppose individual X scores in the population follow a normal distribution N(38, 20). A researcher draws numerous samples of sample size n = 100 from the population, and in each sample, she calculates the sample mean. Then 68% of these sample means should approximately fall within Group of answer choices (A) 34 and 40 (B) 34 and 38 (C) 38 and 44 (D) 36 and 40

Expert Solution

It is given here that , X scores follow a normal distribution with

Each Sample size n = 100

Standard deviation of sampling distribution is , $\sigma_\bar x =$

Substituting values in above formula ,

$\sigma_\bar x =$ = 20/10 = 2

from empirical rule for normal distribution we know that approximately 68% of values of sample mean lies within 1 sigma range from mean value.

So , 68% of these sample means should approximately fall within $\mu \pm 1\sigma_\bar x$

$\mu + 1\sigma_\bar x$ = 38 + 2 = 40 ,

$\mu - 1\sigma_\bar x$ = 38 - 2 = 36

Hence 68% of these sample means should approximately fall within 36 to 40.

Hence correct answer is (D) 36 and 40

milcah answered 1 month ago

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