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Chapter 12: Problem 67
What is the midrange and how is it obtained?
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A random sample of 30 college students is selected. Each student is asked how much time he or she spent on homework during the previous week. The following times (in hours) are obtained: $$ \begin{aligned} &16,24,18,21,18,16,18,17,15,21,19,17,17,16,19,18,15,15, \\ &20,17,15,17,24,19,16,20,16,19,18,17 . \end{aligned} $$ Construct a frequency distribution for the data.
Intelligence quotients (IQs) on the Stanford-Binet intelligence test are normally distributed with a mean of 100 and a standard deviation of 16. Use the 68-95-99.7 Rule to find the percentage of people with IQs below \(68 .\)
A college professor had students keep a diary of their social interactions for a week. Excluding family and work situations, the number of social interactions of ten minutes or longer over the week is shown in the following grouped frequency distribution. Use this information to solve.$$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Number of } \\ \text { Social Interactions } \end{array} & \text { Frequency } \\ \hline 0-4 & 12 \\ \hline 5-9 & 16 \\ \hline 10-14 & 16 \\ \hline 15-19 & 16 \\ \hline 20-24 & 10 \\ \hline 25-29 & 11 \\ \hline 30-34 & 4 \\ \hline 35-39 & 3 \\ \hline 40-44 & 3 \\ \hline 45-49 & 3 \\ \hline \end{array} $$ Among the classes with the greatest frequency, which class has the least number of social interactions?
A random sample of 40 college professors is selected from all professors at a university. The following list gives their ages: $$ \begin{aligned} &63,48,42,42,38,59,41,44,45,28,54,62,51,44,63,66,59,46, \\ &51,28,37,66,42,40,30,31,48,32,29,42,63,37,36,47,25,34, \\ &49,30,35,50 \end{aligned} $$ Construct a stem-and-leaf plot for the data. What does the shape of the display reveal about the ages of the professors?
A set of data items is normally distributed with a mean of 400 and a standard deviation of 50. Find the data item in this distribution that corresponds to the given z-score. \(z=-2.5\)
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