6. Normal Distribution and Continuous Random Variables

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

For the standard normal distribution, what is the area under the curve to the left of $z=1$?

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

Using the standard normal table, what is the probability that $z\ge 1.4$? Round your answer to the nearest percent.

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

The standard normal curve is associated with which normal distribution?

In Exercises 8 and 9, assume that women have standing eye heights that are normally distributed with a mean of 59.7 in. and a standard deviation of 2.5 in. (based on anthropometric survey data from Gordon, Churchill, et al.).

a. If an eye recognition security system is positioned at a height that is uncomfortable for women with standing eye heights less than 54 in., what percentage of women will find that height uncomfortable?

Which of the following is true regarding the standard normal distribution?

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

Assume the random variable $x$ is normally distributed with mean $\mu$ and standard deviation $\sigma$. What is the standard normal variable $z$ corresponding to a value $x$?

For the standard normal probability distribution, the area to the left of the $\mathrm{mean}$ is:

For the standard normal distribution, what $z$-value corresponds to a lower-tail probability of $1\%$?

For a two-tailed hypothesis test at the $5\%$ significance level using the standard normal distribution, what are the critical value(s) for $z$?

For a standard normal distribution, if the probability that a value is less than $z$ is $0.975$, what is the smallest value of $z$ that satisfies this requirement?

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