STAT212
In-Class Exercise
1. Suppose the research department of a steel manufacturer believes that one of the company’s rolling machines is producing sheets of
steel of varying thickness. Assume that the thickness is a uniform random variable with values between 150 and 200 millimeters. Let x
denote the thickness of the sheets produced by this machine.
a. Graph the probability distribution of x.
b. Any sheets less than 160 millimeters thick must be scrapped, since they are unacceptable to buyers. Calculate the fraction of steel
sheets produced by this machine that have to be scrapped.
2. A machine produces bolts whose diameters are approximately normally distributed with an average diameter of .25 inch and a
standard deviation of .02 inch. Find the probability that a randomly selected bolt has a diameter
a. greater than .24 inch.
b. between .2 and .3 inch.
c. less than .19 inch.
3. Scores on a test have a mean of 71 and the score of 80 falls at the 75th percentile. The scores have a distribution that is
approximately normal. Find the score that falls at the 39th percentile.
4. Let x be a normal random variable with =500 and =100. Find k such that P(500 – k < x < 500 + k) = .34.
5. The distribution of resistance for resistors of a certain type is known to be normal, with 10% of all resistors having a resistance
exceeding 10.634 ohms, and 5% having a resistance smaller than 9.7565 ohms. What are the mean value and standard deviation of the
resistance distribution?
6. Let x denote the amount of time for which a book on 2-hour reserve at a college library is checked out by a randomly selected
student and suppose that x has the probability density function
.5 x 0  x  2
f ( x)  
0 otherwise
A student is selected at random.
P(0<x<1) =
7. The results on a certain blood test performed in a medical laboratory are known to be approximately normally distributed, with
=60 and =18.
a.
What percentage of the results are above 65?
b.
What percentage of the results are between 40 and 70?
c.
What percentage of the results are below 70?
d.
What percentage of the results are between 75 and 90?
e.
What percentage of the results are outside the “healthy range” of 20 to 100?
f.
Which result is located at the 40th percentile?