The number of accidents per week at a hazardous intersection varies with mean 2.

Question

The number of accidents per week at a hazardous intersection varies with mean 2.4 and standard deviation 1.5. This distribution takes only whole-number values, so it is certainly not normal (a) Let x be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of x according to the Central Limit Theorem? = 2.4 0.2080 (b) What is the approximate probability that x is less than 2? 0.0281 (c) What is the approximate probability that there are fewer than 120 accidents at the intersection in a year? (Hint: Restate this event in terms of x.) 5279

Explanation / Answer

mean = 2.4
std.dev.(x) = 0.2080

b)
P(X < 2)
= P(z < (2 - 2.4)/0.208)
= P(z < -1.9231)
= 0.027235195

c)
mean = 2.4*52 = 124.8
std.dev. = 1.5*sqrt(52) = 10.8167

P(X < 120)
= P(z < (120 - 124.8)/10.8167)
= P(z < -0.44376)

= 0.3286

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