Quantitative Analysis for management Using Binomial Probability

1. In a production run of 300 units, there are exactly 20 defective items and 280 good items.

(a) What is the probability that a randomly selected item is defective?
(b) If two items are sampled without replacement, what is the probability that both are good?
(c) If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective?

2. Colonel Motors (an automobile company) has prepared a marketing campaign for its best-selling car. The focus of the campaign is quality, and it is claimed that 97 percent of the purchasers of this car have no complaints in the first year. You and your sister Kim have each purchased one of these cars.

(a) What is the probability that neither of you has a complaint about the car in the first year if the advertising claim is true?
(b) What is the probability that exactly one of you has a complaint about the car in the first year if the advertising claim is true

Solution Preview

1. In a production run of 300 units, there are exactly 20 defective items and 280 good items.

(a) What is the probability that a randomly selected item is defective?
P(Defective) = No of defectives / total items produced = 20/300=0.0667

(b) If two items are sampled without replacement, what is the probability that both are ...

Solution Summary

Shows how to calculate the probability under various situations.

Answer the following:
(A) Find the binomialprobability P(x = 6), where n = 15 and p = 0.60.
(B) Set up, without solving, the binomialprobability P(x is at most 6) usingprobability notation.

I need verified on the following questions. Please identify the correct answers.
The primary purpose of quantitativeanalysis should be to gain a greater understanding of the problem, not to automate decision making.
True
False
Managers do not need to be familiar with the limitations, assumptions, and

h-p is said to be the leading seller of pc's in the U.S WITH 27% share of the pc market. if a researcher selects 130 recent pc purchases, use the normal approximation to the binomial to find the probability that more than 39 bought a h-p computer

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomialprobabilityformula to find the probability of x successes given the probability p of success on a single trial.
n = 10, x = 2, p = 1/3

Assume that 12 percent of adults in this country have filed for bankruptcy at some point in their life. If an independent sample of 20 adults is selected find the probability that fewer than 5 will have filed for bankruptcy at some point in their life.

Nathan wants to approximate a binomialprobability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95
Can Nathan use the normal curve area to approximate a binomialprobability?

Objective: Calculate binomial and Poisson probabilities.
1) Chapter 5: Problem 5.5 (binomial)
Solve the following problems by using the binomialformula.
a. If n = 4 and p = .10 , find P(x = 3) .
b. If n = 7 and p = .80 , find P(x = 4) .
c. If n = 10 and p = .60 , find P(x ≥ 7) .
d. If n = 12 and p = .45