Assume that a policyholder is four times more likely to file exactly two claimsas to file exactly three claims. Assume also that the number X of claims of thispolicyholder is Poisson. Determine the expectation E(X²).Suppose that the probability of suffering a side effect from a certain flu vaccineis 0.005. If 1000 persons are inoculated, find the approximate probability that(a) At most 1 person suffers.(b) 4, 5, or 6 persons suffer.

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Answered: Assume that a policyholder is four…

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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In the game of roulette, a player can place a $7 bet on the number 32 and have a 138 probability of winning. If the metal ball lands on 32, the player gets to keep the $7 paid to play the game and the player is awarded an additional $245.Otherwise, the player is awarded nothing and the casino takes the player's $7. Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose.
The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20-39 who regularly skip eating breakfast is 0.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size n = 500 of young adults ages 20-39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, X, in Lance's sample who regularly skip breakfast is greater than 122. You may find table of critical values helpful. Express the result as a decimal precise to three places. P(X > 122)%3D eal limir thaor tnr the hinamialdietrikotian tn indtha neohabilin: tbot the numbar of individuale in Aanly tha nd tems of use contact us he p about us cyeers 6:56 PM 11/6/2020 a. 2) Cip prt sc insert 110 |
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 226 numbers from this file and r = 87 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. 1) Test the claim that p is more than 0.301. Use α = 0.10. 2) What is the value of the sample test statistic? (Round your answer to two decimal places.) 3) Find the P-value of the test statistic. (Round your answer to four decimal places.) 4) If p is in fact larger than 0.301, it would seem there are too many numbers in…
What is the difference between discrete and continuous probability distributions? We will solve this problem with Excel Using BINOMDIST. Suppose that 48% of individuals 85 years and older have Alzheimer’s Disease. You go to a nursing home that has been feeding residents a diet consisting of natural, organic, and healthy foods including free range chickens, omega 3 eggs, flax seed, etc. You find that only 29 of 100 residents who are 85-years and older have Alzheimer’s disease? What is the likelihood of this outcome? Use the formula for the corresponding probability distribution to solve the problem. A manufacturer of television set known that on an average 5% of their product is defective. They sells television sets in consignment of 100 and guarantees that not more than 2 set will be defective. Which probability distribution is appropriate for use in the scenario? What is the value of λ? Write down the formula for the Probability Distribution. What is the probability that the…
The waiting time T at a bank teller’s window between two successive customers isdistributed as exponential with a mean of four minutes. Find the following probabilities:(a) P(T ≥ 5, (b) P(3 ≤ T ≤ 6), (c) P(T ≤ 4), and (d) P(T < 5). NOTE: Please explain each part, so the problem can be used as a Study Guide
In game of roulette, a player can bet on the 1/38 probabilty of metal batt landa on 1the player gets to keep the paid to play the game and the player is awarded an additional 140 Otherwise, the player is awarded nothing and the casino takes the player's $4. Find the expected value E(x) to the player for one play of the game to player in a game of chance, then E(x) is negative. This value gives the average amount the player can expect to lose.
The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 14.9% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? (Round to three decimal places as needed.)
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
In the game of roulette, a player can place a $6 bet on the number 11 and have a ag probability of winning. If the metal ball lands on 11, the player gets to keep the $6 paid to play the game and the player is awarded an additional $210. Otherwise, the player is awarded nothing and the casino takes the player's $6. Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. The expected value is $ (Round to the nearest cent as needed.)

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