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Statistics and Probability

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Moderate

Understanding Central Limit Theorem

STATS-9JLAXG

Let $\bar{X}$ be the experiment of collecting a sample of size 50 from a population with mean $\mu=10$ and variance $\sigma^2=16$.

Consider the following four statements below:

i. The random variable defined by $\dfrac{\bar{X}-10}{\dfrac{4}{\sqrt{50}}}$ is a Standard Normal random Variable.

ii. The variance of $\dfrac{\bar{X}-10}{4}$ is 1.

iii. The probability that the outcome of $\bar{X}$ is smaller than 10 is .5.

iv. The probability that the outcome of $\dfrac{\bar{X}-10}{\dfrac{4}{\sqrt{50}}}$ is smaller than 0 is .5.

A

Statements i and ii are TRUE while iii and iv are FALSE.

B

Statements i, ii, and iii are TRUE and iv is FALSE.

C

Statements i, ii, and iv are TRUE and iii is FALSE.

D

Statements iii, and iv are TRUE and i and ii are FALSE

E

Statement iii is TRUE and i, ii, and iv are FALSE