6. Normal Distribution and Continuous Random Variables

In Exercises 21 and 22, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

Describe the shape of the distribution for the histogram you made in Exercise 3 as symmetric, uniform, skewed left, skewed right, or none of these.

Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences.

Finding Probability In Exercises 47–56, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.

P(- 0.89 < z < 0)

Finding Probability In Exercises 47–56, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.

P(- 1.54 < z < 1.54)

Graphical Analysis In Exercises 11–16, determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

Graphical Analysis In Exercises 11–16, determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

Using and Interpreting Concepts

Finding Area In Exercises 17–22, find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area.

Using and Interpreting Concepts

Finding Area In Exercises 17–22, find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area.

Finding Area

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

To the left of z=0.33

Finding Area

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

To the right of z= -0.355

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

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= -1.55 and z= 1.55

Computing Probabilities for Normal Distributions In Exercises 1–6, the random variable x is normally distributed with mean mu=174 and standard deviation sigma=20. Find the indicated probability.

P(x > 182)

Computing Probabilities for Normal Distributions In Exercises 1–6, the random variable x is normally distributed with mean mu=174 and standard deviation sigma=20. Find the indicated probability.

P(172 < x <192)