Question
A car company wishes to test its cars for a defect which is known to affect...
A car company wishes to test its cars for a defect which is known to affect 2% of cars. Suppose the company randomly (and independently) selects 300 units of the same type of car. Let X be the number of defective cars out of the 300 selected.
(a) What type of RV is X?
(b) Compute the expected number of defective cars.
(c) What is the probability that exactly 6 cars are defective?
(d) What is the probability that up to ±5 from 6 (that is, between 1 and 11 inclusive) cars are defective? (e) How good a guess would ±5 away from 6 be, given our answer for (d)?
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