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 $p(-2.50<z<1.50)$?