The number of accidents per week at a hazardous intersection

The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.8. 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??? Ux-bar =???? (Sigma)x-bar = ???? (b) What is the approximate probability that x-bar is less than 2? (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-bar.)

Solution

30 per year = 130/52 = 2.5 per week
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(2.5-2.2)/1.8 = 0.166
So an average of 2.5 accidents perweek is 0.166 standard deviations
above the mean of 2.2.

The appromate chance the average is less than 2.5 accidents per week

is about 96% or 0.9629...