Simulation Homework on Distributions
Due: Friday, Nov., 7. Turn in at class time, keep a copy, and be prepared to show your
work on the board.
1. IQ scores are normally distributed throughout society with a mean of 100 and a
standard deviation of 15.
A) A person with an IQ of 140 or higher is called a genius. What proportion of society
is in the genius category?
B) What proportion of society will miss the genius category by 5 or fewer points?
C) An IQ of 110 or higher is required to make it through an accredited college or
university. What proportion of society could be eliminated from completing
higher education based on a low IQ score?
2. Service times at a local deli are normally distributed with a mean of 10 minutes and
a variance of 16.
A) What percentage of customers can expect to receive their orders in under 5
minutes?
B) Customer satisfaction surveys indicate that if a person has to wait over 20 minutes
for an order, he will likely not return. What proportion of customers will likely
never return?
C) Joe, the owner, wants all orders filled in under 12.5 minutes. What proportion are
currently filled this quickly?
3. Given the following data.
67
56
73
22
24
87
45
90
12
45
87
98
43
21
8
56
32
81
55
22
6
20
59
43
82
40
25
38
95
33
A) Compute the mean and the standard deviation.
B) Draw a bar-graph with value on the x-axis and the number of occurrences on the
y-axis. Draw one graph with increments of 5 on the x-axis (0-4, 5-9, 10-14,...), then
draw another graph with the values on the x-axis grouped in increments of 10.
4. Many states have license tags which have the following format:
letter letter letter number number number
The letters indicate the weight of the automobile, but the numbers are at random
ranging from 100 to 999. (Random implies uniform distribution.)
A) What is the probability that the next tag seen at random will have a value higher
than 500? (Approximate the discrete uniform distribution with the continuous
uniform.)
B) What is the probability that the next tag seen will be in the 200's?