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

Pearson’s Index of Skewness The English statistician Karl Pearson (1857–1936) introduced a formula for the skewness of a distribution.

P = 3 (x̄ - median) / s

Most distributions have an index of skewness between -3 and 3. When P > 0, the data are skewed right. When P < 0, the data are skewed left. When P = 0, the data are symmetric. Calculate the coefficient of skewness for each distribution. Describe the shape of each.

c. x̄ = 9.2, s = 1.8, median = 9.2

Pearson’s Index of Skewness The English statistician Karl Pearson (1857–1936) introduced a formula for the skewness of a distribution.

P = 3 (x̄ - median) / s

Most distributions have an index of skewness between -3 and 3. When P > 0, the data are skewed right. When P < 0, the data are skewed left. When P = 0, the data are symmetric. Calculate the coefficient of skewness for each distribution. Describe the shape of each.

e. x̄ = 155, s = 20.0, median = 175

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.

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.

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.