Page 164 - Probability Demystified

CHAPTER 9 The Normal Distribution 153

2. Eight students were asked how many hours it took them to write a
research paper. Their times (in hours) are shown: 6, 10, 3, 5, 7, 8, 2, 7.
Find the range and standard deviation.
3. The high temperatures for 10 selected cities are shown: 32, 19,
57, 48, 44, 50, 42, 49, 53, 46. Find the range and standard deviation.
4. The times in minutes it took a driver to get to work last week are
shown: 32, 35, 29, 31, 33. Find the range and standard deviation.
5. The number of hours 8 part-time employees worked last week is
shown: 26, 28, 15, 25, 32, 36, 19, 11. Find the range and standard
deviation.

ANSWERS
1. The range is 16 8 ¼ 8.

8 þ 12 þ 15 þ 16 þ 14 þ 10 þ 10 þ 11 þ 13 þ 15 þ 9 þ 11
The mean is ¼
12
144
¼ 12:
12

The standard deviation is

2
8 12 ¼ 4 ð 4Þ ¼ 16
2
12 12 ¼ 0 0 ¼ 0
2
15 12 ¼ 3 3 ¼ 9
2
16 12 ¼ 4 4 ¼ 16
2
14 12 ¼ 2 2 ¼ 4
2
10 12 ¼ 2 ð 2Þ ¼ 4
2
10 12 ¼ 2 ð 2Þ ¼ 4
2
11 12 ¼ 1 ð 1Þ ¼ 1
2
13 12 ¼ 1 1 ¼ 1
2
15 12 ¼ 3 3 ¼ 9
2
9 12 ¼ 3 ð 3Þ ¼ 9
2
11 12 ¼ 1 ð 1Þ ¼ 1
74
74 p ffiffiffiffiffiffiffiffiffi
¼ 6:73 6:73 ¼ 2:59 ðroundedÞ
11