Question

4. Suppose the event of a student’s application to a university being accepted follows the binomial probability. The successful rate is 80%. Please finish the following tasks?

(1) Determine the expected number of acceptances for the next nine applicants and the standard deviation.

(2) What is the probability that among the next 10 applicants exactly 6 will be accepted?

(Please show the detail computation steps. Please don’t just give an answer from Excel functions or calculator functions. Otherwise, you will not get all the points.)

   [Hint: Please see Chapter 5 – Slides 23 -34 for Binomial Probability Distribution. Please also see related pages in the textbook.]

5.

The random variable x is the number of the number of calls received by a switchboard. Suppose x follows a Poisson distribution and the average number of occurrences in 20 minutes is 2.

(1) What is the probability that between 10:00 and 10:30 the switchboard will receive exactly 5 calls?

(2) What is the probability that between 10:00 and 10:30 the switchboard will receive more than 2 calls but fewer than 6 calls?

(Please show the detail computation steps. Please don’t just give an answer from Excel functions or calculator functions. Otherwise, you will not get all the points.)

   [Hint: Please see Chapter 5 – Slides 35- 40 for Poisson Probability Distribution. Please also see related pages in the textbook.]

6.

A type of multifunction printer produced by ABC Company was found to be defective (D). There are three factories (A, B, C) manufacturing this product (35% from factory A, 35% from factory B, and 30% from factory C). A manager is responsible for investigating the source of found defects. So far the manager knows the following information: P(D | A) = 0.015, P(D | B) = 0.010, P(D | C) = 0.020

The manager would like to answer the following question: If a randomly selected printer is defective, what is the probability that the printer was manufactured in factory A? Also, if a randomly selected printer is defective, what is the probability that the printer was manufactured in factory B?

Answer 1