5.* Car Accidents: Of the reported 1567 car accidents in Stevens County last yea
ID: 3060227 • Letter: 5
Question
5.* Car Accidents: Of the reported 1567 car accidents in Stevens County last year, 923 of them occurr within 1 mile of the person's home. (a) If one of the reported car accidents is randomly selected, what is the probability that it occurr within 1 mile of the person's home? (b) Estimate the probability that the next reported car accident in Stevens County will be within mile of the person's home? 6. Life Insurance: A life insurance company wants to estimate the probability that a 40 year old m will live through the next year. In a random sample of 80,000 such men, 79,968 lived through the year. Using the relative frequency approximation, what is the probability that a randomly selected 40 ye old male will die within a year? 7." Warranty: In setting the warranty price for MP3 players, an electronics company want the probability that a randomly purchased MP3 player will fail within the year. In 4000 randomly so MP3 players, 24 of them the probability that the next MP3 player sold will fail within a year? failed within the year. Using the relative frequency approximation, whatExplanation / Answer
5. Total number of car accidents in the county =1567.
Number of accidents occurring within 1Km of the person's house =923.
(a) Let "A" denote the event that a randomly chosen accident from the list of all 1567 accidents occurs within 1Km of the person's house. Thus, probability of A is:
P(A) =[number of ways the accident chosen randomly is from within 1Km of the person's house]/[total number of possible ways of choosing an accident out of all 1567 accidents in the county]
=> P(A) =(923C1)/(1567C1) =923/1567 =0.5890
=> P(A) =923/1567 =0.5890.
(b) Let us define "success" as the event that an accident occurs within 1Km of the person's house. Then let us use the relative frequency approximation of probability as the probability of success, being denoted by "p".
Thus, P(next reported accident is within 1Km of the person's house) =probability of success =923/1567 =0.5890
=>P(the next accident reported is within 1Km of the person's house) =923/1567 =0.5890.
6. Let us define "success" as the event that a 40 year old male will live through the next year. Using relative frequency approximation to probability, from given information, probability of success, say p =79968/80000 =0.9996
Thus probability that a randomly selected 40 year old male will die within the next year is, in fact, the probability of failure =1-(probability of success) =1-p =1-0.9996 =0.0004.
=> P(a randomly selected 40 year old male will die within the next year) =0.0004.
7. Let us define "success" as the event that an MP3 player of the electronic company actually fails within 1 year of being sold of 4000 randomly sold players, 24 failed within the year.
Thus, probability of success =P(an MP3 player fails within the year) =24/4000 =0.006.
Using the relative frequency approximation of probability, we can say probability that an MP3 player fails within the year id 0.006.
Thus, probability that the next player fails within the year =0.006.
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