Question

In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. The distribution of the sample mean IQ is (a)exactly Normal, mean 112, standard deviation 20. (b)approximately Normal, mean 112, standard deviation 0.1. (c)approximately Normal, mean 112, standard deviation 1.414. (d)approximately Normal, mean 112, standard deviation 20. (e)exactly Normal, mean 112, standard deviation 1.414.

Answer 1

Answer:

(c)approximately Normal, mean 112, standard deviation 1.414.

Step-by-step explanation:

To solve this problem, we have to understand the Central Limit Theorem

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$.

In this problem, we have that:

$\mu = 112, \sigma = 20, n = 200$

Using the Central Limit Theorem

The distribution of the sample mean IQ is approximately Normal.

With mean 112

With standard deviation $s = \frac{20}{\sqrt{200}} = 1.414$

So the correct answer is:

(c)approximately Normal, mean 112, standard deviation 1.414.