6. Normal Distribution and Continuous Random Variables

Graphical Analysis In Exercises 19–22, use the box-and-whisker plot to determine whether the shape of the distribution represented is symmetric, skewed left, skewed right, or none of these. Justify your answer.

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= -1.28 and to the right of z= 1.28

Given the mean of a normal distribution, how can you find the median?

Describe the inflection points on the graph of a normal distribution. At what x-values are the inflection points located?

The data set represents the number of minutes a sample of 27 people exercise each week.

108 139 120 123 120 132 123 131 131

157 150 124 111 101 135 119 116 117

127 128 139 119 118 114 127 142 130

d. Describe the shape of the distribution as symmetric, uniform, skewed left, skewed right, or none of these.

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