6. Normal Distribution and Continuous Random Variables

Suppose $X$ is a standard normal random variable with density function $f\left(x\right)$. What is the value of $P(1<X<4)$?

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.