6. Normal Distribution and Continuous Random Variables

For a normal distribution, which of the following statements is true about the $\mathrm{mean}$, $\mathrm{median}$, and $\mathrm{mode}$?

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

Which of the following is a characteristic of the standard normal probability distribution?

In a standard normal distribution, what is the mean $\mu$ of the distribution?

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

For a standard normal distribution, what is the mean $\mu$ and standard deviation $\sigma$?

Which of the following is a similarity between the $t$ distribution and the standard $z$ distribution?

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

Which of the following statements is true about the standard normal distribution?

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?