91Ó°ÊÓ

Refer to the data of Exercise \(3.109\) on the current annual incomes (in thousands of dollars) of the 10 members of the class of 2000 of the Metro Business College who were voted most likely to succeed. \(\begin{array}{llllllllll}59 & 68 & 84 & 78 & 107 & 382 & 56 & 74 & 97 & 60\end{array}\) a. Determine the values of the three quartiles and the interquartile range. Where does the value of 74 fall in relation to these quartiles? b. Calculate the (approximate) value of the 70 th percentile. Give a brief interpretation of this percentile. c. Find the percentile rank of 97 . Give a brief interpretation of this percentile rank.

A student washes her clothes at a laundromat once a week. The data below give the time (in minutes) she spent in the laundromat for each of 15 randomly selected weeks. Here, time spent in the laundromat includes the time spent waiting for a machine to become available. \(\begin{array}{rrrrrrrr}75 & 62 & 84 & 73 & 107 & 81 & 93 & 72 \\ 135 & 77 & 85 & 67 & 90 & 83 & 112 & \end{array}\) Prepare a box-and-whisker plot. Is the data set skewed in any direction? If yes, is it skewed to the right or to the left? Does this data set contain any outliers?

The test scores for a very large statistics class have a bell-shaped distribution with a mean of 70 points. a. If \(16 \%\) of all students in the class scored above 85, what is the standard deviation of the scores? b. If \(95 \%\) of the scores are between 60 and 80, what is the standard deviation?