Normal Distribution Quiz: Z-Scores & CLT Practice

Question 1

A test score is $x=82$ with mean $\mu=70$ and standard deviation $\sigma=6$. What is the z-score?

Accepted Answer

$z=2$

Answer

$z=-2$

Answer

$z=\frac{12}{70}$

Answer

$z=12$

Question 2

Find the value $x$ such that $P(Z<x)=0.975$ for $Z\sim N(0,1)$ (approximately).

Accepted Answer

$x\approx 1.96$

Answer

$x\approx 2.33$

Answer

$x\approx 1.645$

Answer

$x\approx -1.96$

Question 3

A population is strongly right-skewed with finite mean and variance. You take random samples of size $n=50$. Which statement best describes the distribution of $\bar X$?

Accepted Answer

$\bar X$ will be approximately normal by the CLT, and its mean is $\mu$.

Answer

$\bar X$ is approximately uniform for large $n$ because of averaging.

Answer

$\bar X$ has standard deviation $\sigma\sqrt{n}$, so it becomes more spread out.

Answer

$\bar X$ will be exactly normal because the population is skewed.

Normal Distribution Quiz: Z-Scores & CLT Practice

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