6. Normal Distribution and Continuous Random Variables

Which of the following does not describe the standard normal distribution?

Given the mean of a normal distribution is $\mu$ and the standard deviation is $\sigma$, what is the mean of the corresponding standard normal distribution after standardizing the variable?

For the standard normal distribution, what is the total area under the $N(0,1)$ normal curve?

Finding Area

In Exercises 23–36, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

To the left of z=1.365

For the standard normal distribution, what proportion of the distribution lies between $z=-1.75$ and $z=1.75$?

For the standard normal distribution, what is the total area under the normal curve?

A random variable Z that is normally distributed with mean μ = 0 and standard deviation σ = 1 is said to have the ____________________.

For the standard normal probability distribution, what are the mean $\mu$ and standard deviation $\sigma$?

Student's $t$ distributions are symmetric about a value of $t$. What is that value?

Find the area under the standard normal distribution to the left of a z-score of $1.21$.

Find the area under the standard normal distribution to the right of a z-score of $-0.44$.

Find the area of the shaded region under the standard normal distribution.

Find the z-score such that $P$(Z < z)$=0.6331$.

Find the z-score corresponding to the probability/area shown under the standard normal curve below.

Normal Distribution If the following data are randomly selected, which are expected to have a normal distribution?

a. Weights of Reese’s Peanut Butter Cups