Chapter 4 Work Sheet
(round answers to 3 decimal places)
1. A farm and garden supply store sells fertilizer in 50 pound bags. For each customer purchasing
fertilizer the probability distribution for the number of bags purchased is given below.
Bags
1
2
3
4
5
a.
b.
c.
d.
e.
f.
g.
Prob
0.55
0.35
0.07
0.02
0.01
Verify that this is a valid pmf.
Find the probability that a random customer buys more than 2 bags.
Find the expected number of bags bought.
Find the standard deviation of the number of bags bought.
Find the probability that the number of bags is within 1 standard deviation of its mean.
Suppose two random customers are selected. Find the probability that they each buy 1 bag.
Suppose two random customers are selected. Find the probability that the total number of bags
purchased is at least 8.
2. The Higher Education Research Institute at UCLA surveyed more than 263,000 incoming
freshmen from 385 colleges. 36.7% of first-generation college students expected to
work fulltime while in college. Source: Eric Hoover, The Chronicle of Higher Education,
2/3/2006). Suppose that you randomly pick 8 first-generation college freshmen from the
survey. You are interested in the number that expects to work full-time while in college.
a. In words, define the random Variable X.
b. What kind of distribution does X have and what are its parameters?
c. What values does X take on?
d. Construct the probability distribution function (PDF) for X.
X
P(X=x)
X*P(X=x)
e. On average (µ), how many would you expect to answer yes?
f. What is the standard deviation (σ) ?
g. What is the probability that exactly 6 of the freshmen expect to work full-time?
h. What is the probability that at most 6 of the freshmen expect to work full-time?
i.
What is the probability that exactly 2 of the freshmen expect to work full-time?
j.
Use the table to find the probability that between 2 and 6 (inclusive) of the freshmen
expect to work full-time?
k. Use the your calculator functions to find the probability that between 2 and 6
(inclusive) of the freshmen expect to work full-time?
3. In a certain rural area of New York state, 80% of drivers use chains on the car tires for
winter driving. A random sample of 10 drivers is taken. You are interested in the number
of drivers in the sample that use chains while driving.
a. In words, define the random Variable X.
b. What kind of distribution does X have and what are its parameters?
c. Find the probability that exactly 7 drivers in the sample use chains.
d. Find the probability that at most 7 drivers in the sample use chains.
e. Find the probability that more than 7 drivers in the sample use chains.
f. Find the probability that less than 7 drivers in the sample use chains.
g. Find the probability that at least 7 drivers in the sample use chains.
h. Find the probability that between 5 and 9 (inclusive) drivers in the sample use chains.
i.
Find the average number of drivers in the sample that use chains.
j.
Find the standard deviation of the number of drivers in the sample that use chains.
4. There are 12 marbles in a jug. There are 5 Red, 4 White and 3 Black. A player will
randomly select 6 marbles at random. You are interested in the number of white
marbles selected.
a. In words, define the Random Variable X.
b. What type of distribution does X have and what are its parameters?
c. What values does X take on?
d. Construct the probability distribution function (PDF) for X.
x
P(X = x)
X * P(X = x)
e. On average(µ), how many white marbles do you expect to be selected?
f. Find the probability that exactly 2 white marbles are selected.
g. Find the probability that less than 2 white marbles are selected.
h. Find the probability that all the marbles selected are white.