31) The number of accidents per week at a hazardous intersection varies with mea
ID: 2960171 • Letter: 3
Question
31) The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution takes only whole-number values, so it is certainly not Normal.(a) Let (x-bar) be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of (x-bar) according to the central limit theorem?
(b) What is the approximate probability that (x-bar) is less than 2?
(c) What is the approximate probability that there are fewer than 100 accidents at the intersection in a year? (Hint: Restate this event in terms of (x-bar).
Explanation / Answer
Given mean=2.2, s=1.4
(a) Let (x-bar) be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of (x-bar) according to the central limit theorem?
xbar ~Normal(mean=2.2, s=1.4/52=0.19)
(b) What is the approximate probability that (x-bar) is less than 2?
P(xbar<2) = P((xbar-mean)/s < (2-2.2)/0.19)
=P(Z<-1.05)
= 0.1468 (check standard normal table)
(c) What is the approximate probability that there are fewer than 100 accidents at the intersection in a year? (Hint: Restate this event in terms of (x-bar).
P(X<100) = P(xbar< 100/52)
=P(xbar<1.92)
=P(Z<(1.92-2.2)/0.19)
=P(Z< -1.47)
=0.0708 (check standard normal table)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.