Question

a random sample of 40 college professors is selected from all professors at a university. the following list gives their ages.
65, 42, 41, 43, 37, 56, 45, 48, 47, 20, 52, 68, 53, 43, 67,
69, 52, 47, 54, 24, 37, 64, 42, 44, 32, 35, 42, 38, 20, 44,
65, 33, 38, 42, 29, 34, 49, 36, 32, 55.
construct a stem - and - leaf plot for the data. complete parts a. and b.
a. determine the leaves for each corresponding stem. complete the table below.
(use ascending order.)
stem
2
3
4
5
6
leaves
0049
2,2,3,4,5,6,7,7,8,8
122223344457779
223450
455789
b. what does the shape of the display reveal about the ages of the professors?
a. the greatest number of college professors are in their 40s.
b. if you are younger than 30, you cannot be a college professor.
c. none of the college professors live to be 70 years old.
d. none of the above.

Explanation:

Step1: Determine the leaves for each stem

• For stem \(2\): The data values starting with \(2\) are \(20,20,22,23,24,29\). So the leaves are \(0049\) (from \(20,20,24,29\)) and then \(23\) (but since we are just listing leaves in order, for stem \(2\) leaves are \(0049\) (for \(20,20,24,29\)) and then \(2,3\) (from \(22,23\)) but wait no - actually when we sort all data:

The data set is \(20,20,22,23,24,29,32,33,34,35,36,37,38,38,41,42,42,43,43,44,44,45,47,47,48,49,52,52,53,54,55,56,65,65,67,68,69\)
For stem \(2\) (tens digit \(2\)), the units digits (leaves) are \(0,0,2,3,4,9\) so leaves \(002349\)
For stem \(3\) (tens digit \(3\)): units digits \(2,3,4,5,6,7,8,8\) so leaves \(23456788\)
For stem \(4\) (tens digit \(4\)): units digits \(1,2,2,3,3,4,4,5,7,7,8,9\) so leaves \(122334457789\)
For stem \(5\) (tens digit \(5\)): units digits \(2,2,3,4,5,6\) so leaves \(223456\)
For stem \(6\) (tens digit \(6\)): units digits \(5,5,7,8,9\) so leaves \(55789\)

Step2: Analyze statement A

The greatest number in the data set is \(69\) (so not in \(40s\)), so statement A is false.

Step3: Analyze statement B

If you are younger than \(30\) (i.e., age \( < 30\)), from the data (ages \(20,20,22,23,24,29\)) you can be a college professor, so statement B is false.

Step4: Analyze statement C

Since A and B are false, statement C (“None of the college professors live to be 70 years old” - since max age is \(69\)) is True.

Answer:

C. None of the college professors live to be 70 years old.