a. Prudential Insurance Company provides a multiplicity of insurance policies. Theprobability that claims are made in any financial year is 0.04. A researcher randomlyselects 500 policies. Assume, the claims follows a standard normal distribution, calculatethe probability at most 30 claims are made in a financial year.b. Assume the claim in (a) is a random variable X that follows a Poisson distribution with aparameter μ. Answer the following questions:i.ii.Write down the moment generating function Mx (t)By differentiating My(t), show that the mean and variance of X are both equal toμ.

Answered: a. Prudential Insurance Company…

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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A Poisson distribution with A = 7.4 and æ = 6. Use the probability distribution identified above to calculate the following: a. The probability P(x) for the indicated value of x. P (6) =| Round to 3 significant digits b. The mean and standard deviation of the distribution. Mean (и) SD (0) Round to 3 significant digits
Suppose that all the students registered to the probability and statistics course have to buy textbook. The 28 % of all students demand a new book, on the other hand the other 72 % want a used text book. Consider randomly selecting 40 purchasers.a. What are the mean value and standard deviation of the number who want a new copy of thebook?b. What is the probability that the number who want brand-new books is more than 1.5σ awayfrom the mean value?c. The bookstore has 30 new and 30 used textbooks in stock. If 40 people come in one by one topurchase this text, what is the probability that all 40 will get the type of book they want fromcurrent stock? [Hint: Let X = the number who want a new copy. For what values of X will all 40get what they want?]
8. Final: For recent period of 100 years, there were 530 Atlantic hurricanes. Assume the Poisson distribution is a suitable model, find the probability that less than 3 hurricanes in a randomly selected year. O a. .1901 O b. None of the above O C. .2075 O d. .3701 O e..1016 日田
10. The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 6 students who fail per sem. d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period.e. Calculate the probability that there will be a failing student within the first semester.f. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester?
Suppose that the average loan taken out by small-sized businesses from a commercial bank is $275,000. If the loan sizes are normally distributed with a standard deviation of $25,000, find each of the following: A. The probability that a small-sized business takes out a loan of more than $325,000. B. The probability that a small-sized business takes out a loan between $245,000 & $310,000.
It has been determined that the distribution of faulty products in a factory conforms to Poisson. 2% of the products produced monthly are defective. Calculate the probability of finding 3 defective parts in 250 randomly drawn samples.7a. 0.140b. 0.095c. 0.091D. 0.253to. 0.145
Dr. Wilson is considering investing a fixed sum of money in each of three business ventures. Assume that the probability distribution for the number of successful ventures out of three is as follows: X P(X) 0 .022 1 .194 2 .434 3 .350 What is the expected value for the number of successful ventures? What is the standard deviation for the number of successful ventures? What is the probability that Dr. Wilson will enjoy at least two successful ventures? What is the probability that Dr. Wilson will enjoy no successful ventures?
Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective. Round to four decimal places. OA. 0.9066 OB. 0.0823 OC. 0.0869 OD. 0.0932
The probability is 0.35 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In six traffic fatalities, find the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is a. exactly three; at least three; at most three. b. between two and four, inclusive. c. Find and interpret the mean of the random variable Y. d. Obtain the standard deviation of Y. Only typing answer Please explain step by step
The number of large cracks in a length of pavement along a certain street has a Poisson distribution with a mean of 1 crack per 100 m. What is the probability that there will be exactly 8 cracks in a 700 m length of pavement? O A. 0.224 O B. 0.034 O C. 0.130 O D. 0.065
Assume that the probability of a being born with Genetic Condition B is p=17/60. A study looks at a random sample of 1146 volunteers. 4 Find the most likely number of the 1146 volunteers to have Genetic Condition B. (Round answer to one decimal place.) P = Let X represent the number of volunteers (out of 1146) who have Genetic Condition B. Find the standard deviation for the probability distribution of X. (Round answer to two decimal places.) 0= Use the range rule of thumb to find the minimum usual value µ-20 and the maximum usual value p+20. Enter answer as an interval using square-brackets only with whole numbers. usual values= Question Help: Submit Question Jump to Answer Written Example Message instructor 44°F Clear W S 3 E D 4 Q Search R LL T V G Y 00 H J
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