1. Suppose a quality manager for XYZ Computers has collected the following data on thequality status of disk drives by suppliers. She inspected a total of 700 disk drives andderived the following resultsDrive StatusWorking DefectiveSupplierCompany ACompany BCompany CCompany D120101801550530020(a) Based on these inspection data, what is the probability P (B) of ran- domly selectinga disk drive from Company B?(b) What is the probability P (Defect B) of a defect given that Company B supplied thedisk drive?(c) Suppose a defect has been found. Can we use either P (B) or P (Defect B) derived inparts a and b as the percentage to split the cost of defective driver to supplier B? If not,what is the correct percentage? State your reason clearly.

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Answered: 1. Suppose a quality manager for XYZ…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Given the new fad of health consciousness, a random sample of 400 college students was asked what their preferred type of drink was and whether they took regular or sugar free. The following table gives a two-way classification of the responses. Regular Sugar free TOTALS Juice 210 95 305 Iced Coffee 75 20 95 TOTALS 285 115 400 (a) If one student is selected at random from these 400 students, find the probability that this student (i) Prefers sugar free drinks (ii) Prefers juice (iii) Prefers regular juice (iv) Prefers juice given that it is a sugar free drink. (v) Prefers iced coffee or that drinks must be sugar free. (b) Are the events 'prefers juice' and 'prefers sugar free drinks' independent? Use probabilities to state your answer.
7. a. What is the most likely outcome?b. One person is selected at random from these adults. Find the probability that this person is:(i) In favor of cloning(ii) Male and Female against cloning(iii) In favor of cloning given that the person is female(iv) Male or female in favor of cloning
3. Some parts of California are particularly earthquake prone. Suppose that in one metropolitan area, 25% of homeowners are insured against earthquake damage. Four homeowners are to be selected at random. Let Y be the number among the four that have earthquake insurance. (a) Find the probability distribution of Y. (b) Draw the corresponding probability histogram. (c) What is the most likely value for Y? (d) What is the probability that at least two of the four selected have earthquake insurance?
3
1. The distributional pattern of pulmonate slugs inhabiting Libya was studied in the AIUB Journal of Science and Engineering (Aug. 2003). The number of slugs of a certain species found in the survey area was modeled using the negative binomial distribution. Assume that the probability of observing a slug of a certain species (say, Milax rusticus) in the survey area is 0.2. Let Y represent the number of slugs that must be collected in order to obtain a sample of 10 Milax rusticus slugs. a. Give the probability distribution for Y as a formula. b. What is the expected value of Y? Interpret this value.c. Find P(Y = 25).
5. Based on recent records, the manager of a car painting centre has determined the following probability distribution for the number of customers per day: 1 3 4 P(X = x) 0.05 0.2 0.3 0.25 0.15 0.05 А. f the centre has the capacity to serve three customers per day, what is the probability that one or more customers will be turned away on a given day? В. What is the probability that the centre's capacity will not be fully utilized on a day? С. away is no more than 0.1? By how much the capacity must be increased so the probability of turning customer 2. il
2. Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian. (These values ignore a small number of earths among other races. ) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. (a) draw a completely labeled probability tree for this problem. (b) calculate the overall percent of people who died of diabetes across all the three races. (c) given a randomly selected dead person died of diabetes, what is the probability that he/she was white?
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?
After being rejected for employment, Appa Love learns that the Old West Credit Company has hired only 5 women among the last 25 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women. Help her address the charge of gender discrimination by finding the probability of hiring 5 or fewer women when 25 people are hired, assuming that there is no discrimination based on gender. That is, address the claim that the proportion of females hired is 50%. Use the sample data stated above. a. The null and alternative hypothesis would be: Ho : μ 0.5 H₁: p > 0.5 H₁ μ Σ+ Σ Α
4. There are 4 red balls, 6 blue balls and 2 white balls in a bag. Suppose on every single turn, you randomly select a ball, see the color of it and put it back in the bag. You keep doing this repeatedly. a. What is the probability that you get the first red ball on the 5th turn? b. How many turns are expected to get one non-white ball? c. What is the variance of the number of turns required to get one blue ball?

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