Download Bin. Examples

Examples CH 4
1.
Calculate the mean for the discrete probability distribution
shown here.
X
2
P(X) .2
4
.2
5
.3
10
.2
Answer: µ = Σxp(x) = 2(.2) + 4(.3) + 5(.3) + 10(.2) = 5.1
2. Ladies Home Journal polled its readers to determine the
proportion of wives who, if given a second chance, would
marry their husband. According to the responses from the
survey, 80% of wives would marry their husbands again.
Suppose a random and independent sample of n = 20 wives is
collected. Define the random variable X = the number of the
20 wives who would marry their husband again. Then we know
X is a binomial random variable. Find the probability that
more than 15 of the wives responded that they would marry
their husbands again.
Answer: Let a success be a wife who would marry her husband
again.
Then x is a binomial random variable with n = 20 and p =
.80.(Use Table)
P(X > 15) = 1 - P(X ≤ 15) = 1 - .370 = .630
3.
It has been stated that 20% of the general population donate
their time and energy to working on community projects.
Suppose 20 people have been randomly sampled from a community
and asked if they donated their time and energy to community
projects. Let x be the number of them that do donate their
time and energy to community projects. Find the probability
that more than seven of the 20 do donate their time and
energy to community projects.
Answer: Let X is a binomial random variable with n = 20 and p
= .20. (Use Table)
P(x > 7) = 1 - P(x ≤ 7) = 1 - .968 = .032
4. An automobile manufacturer has determined that 30% of all
gas tanks that were installed on its 1988 compact model are
defective. If 15 of these cars are independently sampled,
what is the probability that more than half need new gas
tanks?
Answer: Let x = the number of the 15 cars with defective gas
tanks. Then x is a binomial random variable with n = 15 and p
= .30. (Use Table)
P(more than half) = P(x > 7.5) = P(x ≥ 8) = 1 - P(x ≤ 7) =
1 - .950 = .050
5.
A local newspaper claims that 60% of the items advertised in
its classified advertisement section are sold within 1 week
of the first appearance of the ad. To check the validity of
the claim, the newspaper randomly selected n = 25
advertisements from last year's classified advertisements and
contacted the people who placed the ads. They found that x =
13 of the 25 items sold within a week. Based on this claim,
is it likely to observe x ≤ 13 who sold their item within a
week?
Answer:
Let x = the number of the 20 ads that resulted in the
item being sold within a week.
Then x is a binomial random variable with n = 25 and p = .60.
(Use Table)
P(x ≤ 13) = .268