The probability of being in a car accident when driving more than 10 miles over
ID: 3236650 • Letter: T
Question
The probability of being in a car accident when driving more than 10 miles over the speed limit in a residential neighborhood is 0.07. Of the next 984 cars that pass through a particular neighborhood, what are the first and third quartiles for the number of car accidents in this neighborhood? (Round standard deviation and your final answers to 2 decimal places.)
The probability of being in a car accident when driving more than 10 miles over the speed limit in a residential neighborhood is 0.07. Of the next 984 cars that pass through a particular neighborhood, what are the first and third quartiles for the number of car accidents in this neighborhood? (Round standard deviation and your final answers to 2 decimal places.)
Explanation / Answer
Let X denote the number of car accidents when driving more than 10 miles over the speed limit in a residential neighborhood, then X follows Binomial distribution with n=984 and p=0.07. As n is large, so X follows normal distribution with mean=np=984*0.07=68.88 and standard deviation=sqrt(n p(1-p))=sqrt(984*0.07*(1-0.07))=8.00
So, Q1=63.48 using excel function =NORMINV(0.25,68.88,8.00)
And Q3=74.28 using excel function =NORMINV(0.75,68.88,8.00)
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