Suppose that the probability that a particular bolt has a defect is 0.03 (you ma

Question

Suppose that the probability that a particular bolt has a defect is 0.03 (you may assume this probability does not change), and that 1000 independent bolts were randomly sampled (a) Approximate the probability that no more than 4% of the 1000 bolts have defects (without the continuity correction (b) Approximate the probability that no more than 4% of the 1000 bolts have defects (with the continuity correction (c) Approximate the 5th and 95th percentiles of the total number of bolts that will have defects. (d) If the actual probability in (a)/(b) was 0.9697792, calculate the absolute error for (a)/(b)

Explanation / Answer

Solution

P(bolt has a defect) = 0.03, n = 1000

X follows normal with mean = np = 1000*0.03 = 30 and variance = 29.1

(a) P(X<=0.04) = P(Z< (40-30)/29.10.5) = P(Z<1.85) = 0.9678

(b) P(X<=40) = P(X<40.5) = P(Z<1.95) = 0.9744

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