# MCQs: Binomial Probability

Your company's internal auditor believes that 10% of the company's invoices contain errors. To check this theory, 20 invoices are randomly selected and 5 are found to have errors.

What is the probability that of the 20 invoices written, five or more would contain errors if the theory is valid?

a. .0433

b. .0319

c. .9567

d. .8660

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that: Fewer than two troubles will be repaired on the same day?

a. .6328

b. .0010

c. .0156

d. .0146

A multiple-choice test has 30 questions and each one has five possible answers, of which one is correct. If all answers were guesses, find the probability of getting exactly four correct answers.

a. .0604

b. .1325

c. .2552

d. .8000

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#### Solution Summary

The solution provides step by step method for the calculation of binomial probabilities. Formula for the calculation and Interpretations of the results are also included.

This posting provides solution to statistics MCQs focusing on probability, binomial probability distribution, normal probability concepts, etc

Please show all work and examples

1. Under certain conditions, it is possible that the sum of the probabilities of all the sample points in a sample space is less than one. ___ T/F

2. A compound event formed by use of the word and requires the use of the addition rule. ____ T/F

3. In any binomial probability experiment, independent trials mean that the result of one trial does not affect the probability of success of any other trial in the experiment. ___ T/F

4. The sum of all probabilities in any discrete probability distribution is not always exactly one, since some of the probabilities may be slightly larger than one. ___ T/F

5. If a random variable z is the standard normal score, then the standard deviation of the distribution is 1. ____ T/F

6. Every binomial distribution may be approximated reasonably by an appropriate normal distribution ___ T/F

7. If P(A) = 0.45, P(B) = 0.35, and P(A and B) = 0.25, then P(A | B) is:

A. 1.4

B. 1.8

C. 0.714

D.0.556

8. Which of the following is a characteristic of a binomial probability experiment?

A. Each trial has at least two possible outcomes

B. P(success) = P(failure)

C. The binomial random variable x is the count of the number of trials that occur

D. The result of one trial does not affect the probability of success on any other trial

9. If the random variable z is the standard normal score, which of the following probabilities could easily be determined without referring to a table?

A. P(z > 2.86)

B. P(z < 0)

C. P(z < - 1.82)

D. P(z> -0/5)

10. In which of the following binomial distributions is the normal approximation appropriate?

A. n = 50, p = 0.01

B. n = 500, p = 0.001

C. n = 100, p = 0.05

D. n = 50, p = 0.02