1. In a certain manufacturing company, a production line has 0.25 probability of having a defectiveproduct. If the company has 5 sets of production line,a. What is the probability that exactly 2 of the production line have a defective product?b. What is the expected value of having a defective product?c. What is the probability of at least 2 production line with defective product?

Formula : Binomial distribution is given by

Answered: 1. In a certain manufacturing company,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Assume that there is a 9% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? a. With two hard disk drives, the probability that catastrophe can be avoided is (Round to four decimal places as needed.)
Suppose a shipment of 110 electronic components contains 4 defective components. To determine whether the shipment should be accepted, a quality-control engineer randomly selects 4 of the components and tests them. If 1 or more of the components is defective, the shipment is rejected. What is the probability that the shipment is rejected? The probability that the shipment is rejected is (Round to four decimal places as needed.)
Suppose a shipment of 140 electronic components contains 4 defective components. To determine whether the shipment should be accepted, a quality-control engineer randomly selects 4 of the components and tests them. If 1 or more of the components is defective, the shipment is rejected. What is the probability that the shipment is rejected? The probability that the shipment is rejected is (Round to four decimal places as needed.)
A machine produces items one by one and independently. It is considered that 10% of them are defective. If the machine stops when it produces the fourth defective item:a. What is the expected number of items produced until the machine stops?b. What is the probability that the machine will stop at the tenth article produced?c. What is the probability that it produces at least 10 items for the machine to stop?
6. Clinical trials have shown that 90% of the patients with severe migraine experience relief of their pain after taking the drug Nimodipine. Suppose 15 migraine patients try Nimodipine. a. What is the probability all of the patients experience relief? b. What is the probability only 10 patients experience relief? What is the probability at least 12 patients experience relief? d. What is the probability at most 10 patients experience relief? e. How many are expected to experience relief?
In a certain manufacturing company, a production line has 0.25 probability of having a defective product. If the company has 5 sets of production line, a. What is the probability that exactly 2 of the production line have a defective product? b. What is the expected value of having a defective product? c. What is the probability of at least 2 production line with defective product?
Assume that there is a 8% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? a. With two hard disk drives, the probability that catastrophe can be avoided is 0.9936. (Round to four decimal places as needed.) b. With four hard disk drives, the probability that catastrophe can be avoided is ☐ (Round to six decimal places as needed.)
3. Assume that 12% of people are left-handed. You are trying to find 3 left-handed individuals to interview for an article. Assuming that everyone you approach is willing to be interviewed ... a) what is the probability that you need to approach exactly 6 people to find 3 left-handed individuals? b) what is the probability that you need to approach 6 or more people to find 3 left-handed individuals? c) what is the expected value of the number of individuals that you will need to approach to find 3 left- handed individuals?
7. State College is playing a rival team for the football championship. If State's first- string quarterback is healthy, State College has a 75% chance of winning. If they have to start their backup quarterback, their chances of winning drop to 40%. The team physician says that there are a 70% chance that the first-string quarterback will play. a. What is the probability that State will win that game? b. Suppose that you miss the game but you read in the headlines of Sunday's paper that State won. What is the probability that the second-string quarterback started?
3. A study conducted at a large hospital found that 27.8 percent of all patients admitted to the hospital's ICU remained in the ICU for less than 24 hours. (A) If 8 patients are selected at random from the ICU patients at the hospital, what is the probability that 2 or fewer of them remained in the ICU for less than 24 hours? (B) Suppose that 20 patients are selected at random from the ICU patients at the hospital. Calculate the mean and standard deviation of the number of these patients who remained in the ICU for less than 24 hours. (C) Another result of the study was that for elective (non-emergency) admissions to the hospital's ICU, the length of the stay in the ICU had a mean of 18.9 hours and a standard deviation of 3.9 hours. Assuming that the length of stay in the ICU for elective admissions is normally distributed, what proportion of elective admissions remained in the ICU for less than 24 hours?
An unreliable company produces a large shipment of blenders where 13% have a defective motor, and 25% have a defective electrical cord and 5% have both defects. If you randomly select a blender in this shipment, find the probability that it has... a) only a defective electrical cord. Write your answer as a percent rounded to 1 decimal place. b) a good motor. Write your answer as a percent rounded to 1 decimal place. c) a good motor and a good electrical cord. Write your answer as a percent rounded to 1 decimal place.

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