(Answered) A factory produces xn gadgets on day n where the xn are

Statistics

A factory produces Xn gadgets on day n where the Xn are independent and identically distributed random variables, with mean 5 and variance 9.

(a) Approximate the probability that the total number of gadgets produced in 100 days is less than 440.

(b) Find approximately the largest value of n such that P(X1 + X2 + ... Xn ≥ 200 + 5n ) ≤ 0.05'.

(c) Let N be the first day on which the total number of gadgets produced exceeds 1000. Calculate an approximation to the probability that N ≥ 226.

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