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.

It is estimated that 10 percent of those taking the quantitative methods portion of the CPA examination fail that section. Sixty students are taking the exam this Saturday.
a. How many would you expect to fail? What is the standard deviation?
b. What is the probability that exactly two students will fail?
c. What is the proba

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.

Find the indicated probabilities.
a. P (z > -0.89)
b. P (0.45 < z < 2.15)
Write the binomialprobability as a normal probabilityusing the continuity correction.
BinomialProbability Normal Probability
c. P ( x ≤ 56) P ( x < ? )
d. P ( x = 69 ) P ( ? < x < ?

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

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.
(C) How would you find the normal approximation to the binomialprobability P(x = 6) in part A? Please show how you would calculate

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

Approximately 25% of the population belongs to a health maintenance organization (HMO). Assume that for a randomly selected group of 20 adults, the number belonging to an HMO has a binomial distribution.
The probability of finding exactly 5 in the 20 who belong to an HMO is....
The probability of finding at least one in th

Find a simple algebraic relationship between the negative binomialprobability
P(x) = ((x-1)!/(n-1)!(x-n))*(P^n)(1-p)^x-n for x = n, n + 1, .. and the binomialprobabilityfor the probability of n successes in x trials.

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