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IM 3
The Normal Distribution
Name _______________
1. A certain type of light bulb has an average life of 500 hr, with a standard deviation of 100 hr. The
length of life of the bulb can be closely approximated by a normal curve. An amusement park buys and
installs 10,000 such bulbs. Find the total number that can be expected to last for each of the following
periods of time.
a) At least 500 hr
b) Less than 740 hr
c) Between 650 and 780 hr
d) Between 290 and 540 hr.
2. The scores of soda a machine dispenses into cups is normally distributed with a mean of 250 milliliters
and a standard deviation of 8 milliliters. If one cup of soda dispensed by this machine is randomly
selected, find the following probabilities:
a) Find the probability that the cup contains more than 238 milliliters of soda.
b) Find the probability that the cup contains between 234 and 262 milliliters of soda.
3. The first National Health and Nutrition Exam Survey reported that the average body mass index (BMI)
in the 25 to 39 age group for women was found to be 24 with a standard deviation of 5. If a woman from
this age group is selected at random, what is the probability she has a BMI:
a) between 22 and 30
b) between 32 and 35
c) greater than 35
d) less than 20
4. A measure of the knee range of motion is a normally distributed variable. The mean number of
degrees of knee flexion was 132 degrees with a standard deviation of 10 degrees. If a person is selected at
random, find the probability that the knee flexion of that person is:
a) between 125 and 140 degrees
b) between 145 and 155 degrees
c) greater than 160 degrees
d) less than 110 degrees
5. The average GMAT scores for students entering the graduate school of business at UGA was 631.
Assuming scores are normally distributed and the standard deviation is 80, find the following:
a) P(x > 500)
b) P(x > 600)
c) P(x > 700)
d) The probability that a student scored below 500
e) The probability that a student scored between 500 and 700.