The number of accidents per week at a hazardous intersection varies with mean 2.1 and standard deviation 1.4. 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?
x is approximately N(2.1, 1.4/√52) . .
(b) What is the approximate probability that x is less than 1.9? (Use 3 decimal places.)
(c) What is the approximate probability that there are fewer than 92 accidents at the intersection in a year? (Hint: Restate this event in terms of x. Use 3 decimal places.)