6. Normal Distribution and Continuous Random Variables

Given a standard normal variable $z$, what is the value of $P(z<0)$?

For the standard normal distribution, what is the probability that $0.6\le z\le 2.12$? Choose the closest value.

Which of the following best describes the shaded region on a standard normal distribution curve that corresponds to the probability $P(a<z<b)$?

If Cynthia's test score is $1.5$ standard deviations above the mean, what is her $z$-score in the standard normal distribution?

Which of the following accurately describes the proportions in the tails of a standard normal distribution?

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?

Daily Commute About 83% of U.S. employees drive their own vehicle to work. You randomly select a sample of U.S. employees. Find the probability that more than 100 of the employees drive their own vehicle to work. (Source: U.S. Bureau of Labor Statistics)

c. You select 150 U.S. employees.

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 1 and 2, use the normal curve to estimate the mean and standard deviation.

In Exercises 5 and 6, find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area.

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