(5)
University of Winnipeg Collegiate
Senior 4 Applied Mathematics (40S)
Summer Session 2002
27
Name: ______________________
Date: _______________
Instructions: 1) SHOW
provided.
2) Neatness and clarity of expression will be considered when this paper is evaluated.
3) You are allowed a half sheet of 8 1 /
2
" x 11" paper with notes on one side for this test.
4) Good Luck
Values:
1. The following data represents the time spent in a doctor's waiting room in minutes.
2.5 12.5 15 3 4.5
13 16 10 6 9
10.5 11 15 5 15.5
15 20 35 11 15
6 10 25 3.5 9
8 15 20 5 7
Find the mean and standard deviation of the data. Is the data normally distributed? Justify your answer with your knowledge of the normal curve.
Page 1 of 5

University of Winnipeg Collegiate
Senior 4 Applied Mathematics (40S)
Summer Session 2002
2. Twenty-five people at a local shopping mall were asked to hit a golf ball with a driver. The length of the drive was recorded.
Twenty-five golfers at a private golf course on the day of the club championship were asked to do the same thing. Which group of people would you expect to have the lower standard deviation?
Explain.
(3)
(5)
3. The amount of caffeine consumed daily by a group of people was recorded and found to be normally distributed. The mean was 400 mg and the standard deviation was 30 mg.
Find daily. Find the z -score for someone who consumes 360 mg of caffeine daily. What is the probability that between 360 mg and
415 mg of caffeine are consumed daily? Justify your answer and include a sketch of the normal curve.
Page 2 of 5

(3)
University of Winnipeg Collegiate
Senior 4 Applied Mathematics (40S)
4.
Summer Session 2002
The table shows the mean and standard deviation for the final course marks for three Senior 4 courses.
English 60 14
Physics 59 8
French 75 13
Dave scored 65 in all three subjects. Assuming the scores are normally distributed, how does Dave compare to other students in each of the three courses?
Page 3 of 5

(4)
(3)
University of Winnipeg Collegiate
Senior 4 Applied Mathematics (40S)
5.
Summer Session 2002
A manufacturer of can drink containers finds that on average 3% of the containers are over-sized. A quality control inspector selects
700 containers at random. What is the probability that 25 or more are over-sized?
6. Sam surveyed 150 randomly selected households in Winnipeg to see if any members of the household watched the Bombers lose on
Saturday to Montreal. Ninety-four respondents said yes.
State the 95% confidence interval for the percent of households in
Winnipeg who watched the Bombers lose on Saturday night. What is the margin of error? Justify your answer.
Page 4 of 5

(4)
University of Winnipeg Collegiate
Senior 4 Applied Mathematics (40S)
7.
Summer Session 2002
Explain how to use the TI-83 graphing calculator to find the mean and standard deviation for a set of data.
A machine is programmed to fill sacks with grain. The masses are normally distributed about a mean of 114 kg.
Tests show that 10% of the bags have masses greater than
116 kg. Find the standard deviation.
(2)
Page 5 of 5