6. Normal Distribution and Continuous Random Variables

Outliers For the purposes of constructing modified boxplots as described in Section 3-3, outliers are defined as data values that are above Q3 by an amount greater than 1.5 x IQR or below Q1 by an amount greater than 1.5 x IQR, where IQR is the interquartile range. Using this definition of outliers, find the probability that when a value is randomly selected from a normal distribution, it is an outlier.

Red Blood Cell Count Use the normal distribution in Exercise 16.

a. What percent of the adult males have a red blood cell count less than 6 million cells per microliter?

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

Finding Area

In Exercises 23–36, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

Between z=0 and z=2.86

Approximating Binomial Probabilities In Exercises 19–26, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities. Identify any unusual events. Explain.

Social Media A survey of Americans found that 55% would be disappointed if Facebook disappeared. You randomly select 500 Americans and ask them whether they would be disappointed if Facebook disappeared. Find the probability that the number who say yes is (a) less than 250

In Problems 5–12, find the indicated areas. For each problem, be sure to draw a standard normal curve and shade the area that is to be found.

Determine the total area under the standard normal curve

a. to the left of z = –2 or to the right of z = 2

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 $P(1<X<4)$?