6. Normal Distribution and Continuous Random Variables

If an observation has a z-score of $z=0$ in the standard normal distribution, what does this indicate about the observation's value relative to the mean?

If a random variable is normally distributed with a mean of $0$ and a standard deviation of $1$, what is this distribution called?

For the standard normal distribution, what is the area under the curve between $z=0.0$ and $z=1.79$?

For a standard normal distribution, what is the probability that $z>1.75$?

Which of the following is a property of the standard normal distribution?

Which of the following data sets best approximates a 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 area to the right of $1$ (that is, $P(Z>1)$)?

Using the standard normal distribution, what is the value of $P(0<z<2.25)$?

Suppose the random variable $Z$ follows a standard normal distribution. What is the area under the standard normal curve to the left of $Z=1$?

In a standard normal distribution, what percentage of the data falls within one standard deviation of the mean (that is, between $-1$ and $1$ on the $z$-score scale)?

In the $standardnormal$ distribution, what happens to the graph of the normal curve as the mean $\mu$ increases while the standard deviation $\sigma$ remains constant?

Assume $x$ is normally distributed with a mean of $10$ and a standard deviation of $2$. What is the z-score for $x=14$?

For a standard normal distribution, which of the following variables always equals $0$?

Which of the following best describes a key difference between the $t$-distribution and the standard normal ($z$) distribution?