10. Use the Poisson approximation to determine the following binomial probabilities. If the probability that a person has a certain heart defect is 0.0012, what is the probability that (a) among two thousand people (randomly chosen) at least two have this heart defect? (b) On average, 99.4% of cars have safe brakes when new. What are the probabilities that among a group of 600 new cars (assumed to be “randomly selected"): (i) all have safe brakes; (ii) no more than 598 cars have safe brakes.

10. Use the Poisson approximation to determine the following binomial probabilities. If the probability that a person has a certain heart defect is 0.0012, what is the probability that (a) among two thousand people (randomly chosen) at least two have this heart defect? (b) On average, 99.4% of cars have safe brakes when new. What are the probabilities that among a group of 600 new cars (assumed to be “randomly selected"): (i) all have safe brakes; (ii) no more than 598 cars have safe brakes.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

1.State Farm Insurance studies show that in Colorado, 64% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 12 property damage claims involving automobiles are selected at random. (a) Let r be the number of claims made by males under age 25. Make a histogram for the r-distribution probabilities. (b) What is the probability that three or more claims are made by males under age 25? (Use 3 decimal places.)(c) What is the expected number of claims made by males under age 25? What is the standard deviation of the r-probability distribution? (Use 2 decimal places.) ? ? 2.A professor determines a final grade based on attendance, two papers, three major tests, and a final exam. Each of these activities has a total of 100 possible points. However, the activities carry different weights. Attendance is worth 6%, each paper is worth 8%, each test is worth 19%, and the final is worth 21%. (a) What is the average for a…
3. Consider a property market where the price of your apartment is mod- elled by a binomial random variable. Under current market conditions, the probability that the value of your apartment increases in value by 5% (of its original value) in one month is 0.45. The probability that it decreases in value by 5% (of its original value) in one month is 0.55. Given your past experience with lockdowns and apartment living, you decide to relocate to a regional area in 6 months time. Let X denote the number of increases in the price of your apartment over these 6 months. (a) Find E(X) and o(X). (b) Let Y be the random variable which models the percentage change in the price of your apartment. Then Y = 0.05.X-0.05(6-X) because 0.05.X is the total percentage increase in price and 0.05(6- X) is the total percentage decrease in price. Simplify the expres- sion for Y in terms of X. Then using (a), find E(Y) and o(Y).
1. Twelve electric bulbs are drawn independently every hour from a production line at a factory. The number of defective bulbs are random and independent. Suppose that the probability that a bulb is defective is 0.06. a. What is the probability that less than two bulbs are defective? b. What is the probability that three bulbs tested are the second defective bulbs detected?
1) The population of SAT scores is normal with u- 500 and a - 100. If you get a sample of n 25 students, what is the probability that the sample mean will be greater than M-540?
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?
2. In a recent poll, 81% of parents with children under 18 years of age said that it is more difficult to raise children now. Assume that this percentage is true for the current population of all parents with children under 18 years of age. You take a random sample of 1000 such parents. Using the binomial probability formula: a) Find the probability that from within the sample 800 or less will hold the same view. b) Find the probability that from within the sample, 800 to 830 will hold the same view.
The probability that a person who identifies as male will be color-blind is 0.036. Find the probabilities that in a group of 54 people who identify as male, the following will be true. (a) Exactly 5 are color-blind. (b) No more than 5 are color-blind. (c) At least 1 is color-blind.
Suppose that you want to compare the means of several treatments in a randomized block ANOVA. If given the choice between using the randomized block ANOVA test and the Friedman test, which one would you choose if outliers occur in the sample data? Explain your answer.
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?
4. An agency employs three consulting firms, A, B and C, with probabilities 0.25, 0.3 and 0.45, re- spectively. It is known that the probability of cost overruns for the firms are 0.07, 0.05 and 0.03, respectively. What is the probablity that a cost overrun experienced by the agency involved firm B? Write your final answer in 2 decimal places.
12.)The survival rate for trees planted at a particular landscaping company has been 83% in the past. (a) What is the probability that 9 of the next 12 trees planted will survive? (b) What is the probability that no more than 9 of the next 12 trees planted will survive? (c) What is the probability that at least 9 of the next 12 trees planted will survive? (d) What is the probability that 6 to 9 (at least 6 but no more than 9) of the next 12 trees survive? (e) How many of the next 12 trees planted would you expect to survive?