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Consider each of the following random variables $Y$ and identify which (possibly more than one) are standard normal random variables. Select ALL that apply.

A

$Y$ has mean=0 and variance=1.

B

$Y=\dfrac{X-5}{10}$ where $X$ is a Normal random variable with mean=5 and variance=100.

C

$Y$ is the mean of a sample of size 49 that will be collected from a population with mean=5 and variance=49.

D

$Y=\dfrac{\bar{X}-5}{\dfrac{10}{7}}$ where $\bar{X}$ is the mean of a sample of size 49 that will be collected from a population with mean=5 and variance=100.

E

$Y$ has a probability density function which is bell-shaped and centered at zero.

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