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MAT 155 Lab 5
Sections 5.1-5 Standard Normal; Applications; Central Limit Theorem
Date: ____________
Page 1 of 2
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Lab5NormalDistribution-1.doc
minimum  maximum
range
and σ =
. Find the mean and
2
12
standard deviation for the uniform distribution represented in the figure below. Show the proper work to justify
your answers.
1. In a continuous uniform distribution, µ =
14
26
2. Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. Sketch and
properly label a bell-shaped curve for parts (a) and (b). Show proper work to justify your answers.
(a) If P(0 < z < a) = 0.3907, find a.
(b) If P(x > b) = 0.9922, find b.
3. Based on survey data from Gordon, Churchill, et al., women have forward grip reaches that are normally
distributed with a mean of 27.0 inches and a standard deviation of 1.3 inches. Design engineers decided that
the CD player should be placed so that it is within the forward grip reach of 95% of women. Find the forward
grip reach that separates the 95% of women with the longest reach from the others. Use Table A-2. Make a
sketch, label it properly, and show your work to justify your answer.
MAT 155 Lab 5
Sections 5.1-5 Standard Normal; Applications; Central Limit Theorem
Page 2 of 2
4. A teacher informs her psychology class that a test is very difficult, but the grades will be curved. Scores for the
test are normally distributed with µ = 25 and σ = 5. SHOW your work to justify your answers.
(a) If she curves by adding 50 to each grade, what is the new mean? What is the new standard deviation?
(b) If the original scores are curved as follows, find the numerical limits (to nearest whole number) to fill in the
blank spaces for each letter grade. [HINT: You may want to use your calculator with the invNorm function.]
Letter grade
F
D
C
B
A
% of scores below 0%
10%
30%
70%
90%
100%
Numerical score
0
5. Assume that men’s weights are normally distributed with µ = 172 lbs and σ = 29 lbs. Draw and label an
appropriate sketch for each problem. Use calculator, Table A-2, or computer. SHOW your work, function
used and values entered for each problem.
(a) If a man is randomly selected, find the probability that he has a weight between 160 lbs and 180 lbs.
(b) If 4 men are randomly selected, find the probability that they have a mean weight between 160 lbs and 180
lbs.
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