# Tutoring on the Normal Distribution

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Deliverable 02  Worksheet
Instructions: The following worksheet is shown to you by a student who is asking for help. Your
job is to help the student walk through the problems by showing the student how to solve each
problem in detail. You are expected to explain all of the steps in your own words.
Key:



– This problem is an incorrect. Your job is to find the errors, correct the errors, and
explain what they did wrong.
– This problem is partially finished. You must complete the problem by showing all
steps while explaining yourself.
– This problem is blank. You must start from scratch and explain how you will
approach the problem, how you solve it, and explain why you took each step.
1) Assume that a randomly selected subject is given a bone density test. Those tests
follow a standard normal distribution. Find the probability that the bone density score for
this subject is between -1.93 and 2.37
Students answer: We first need to find the probability for each of these z-scores using
Excel.
For -1.93 the probability from the left is 0.0268, and for 2.37 the probability from the left is
0.9911.
Continue the solution:
Finish the problem giving step-by-step instructions and explanations.
2) The U.S. Airforce requires that pilots have a height between 64 in. and 77 in. If
womens heights are normally distributed with a mean of 63.8 in. and a standard deviation
of 2.6 in, find the percentage of women that meet the height requirement.
3) Womens pulse rates are normally distributed with a mean of 69.4 beats per minute
and a standard deviation of 11.3 beats per minute. What is the z-score for a woman
having a pulse rate of 66 beats per minute?
Let ? =
? =
(?-?)
?
69.4 – 66
11.3
? = 0.03
Corrections:
Enter your corrections and explanations here.
4) What is the cumulative area from the left under the curve for a z-score of -1.645? What is
the area on the right of that z-score?
5) If the area under the standard normal distribution curve is 0.8980 from the right, what
is the corresponding z-score?
Students answer: We plug in =NORM.INV(0.8980, 0, 1) into Excel and get an area of 1.27.
Corrections:
Enter your corrections and explanations here.
6) Manhole covers must be a minimum of 22 in. in diameter, but can be as much as 60
in. Men have shoulder widths that are normally distributed with a mean of 18.2 and a
standard deviation of 2.09 in. Assume that a manhole cover is constructed with a
diameter of 22 in. What percentage of men will fit into a manhole with this diameter?
Students answer: We need to find the probability that men will fit into the manhole. The
first step is to find the probability that the mens shoulder is less than 22 inches.
Continue the solution:

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