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with mean 1.6 flaws per sąuare yard and standard deviation 1.2 flaws per sąuare yard. This population distribution cannot be normal, because a count takes only whole-number values. An inspector studies 200 sąuare yards of the materiał, records the number of flaws found in each sąuare yard, and calculates x, the mean number of flaws per sąuare yard inspected. Use the central limit theorem to find the approximate probability that the mean number of flaws exceeds 2 per sąuare yard.

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 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?

(b)    What is the approximate probability that x 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.)