6. Normal Distribution and Continuous Random Variables

Given a standard normal distribution, what is the area under the curve to the left of $1.00$?

Which of the following is a similarity between the $t$-distribution and the standard normal ($z$) distribution?

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

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

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

For the standard normal distribution, what percentage of the area under the curve lies within one standard deviation of the mean (that is, between $\mu -\sigma$ and $\mu +\sigma$)?

Given a standard normal distribution, what is the area to the left of $1.25$? (Round your answer to 4 decimal places.)

Using the standard normal distribution, what is the value of $p(-2.50<z<1.50)$?

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

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?