Question: A machine produces bolts, of which 10% are defective. Find the probability that in a random sample of 400 bolts produced by the machine, at the most 30 will be defective. Steps to derive 1 The probability for a bolt to be defective, p 1 10 q p 9 10 n 2 n·p 1 10 n·q 9 10 3 Mean, μ = n·p 1 10 4 Standard Deviation, σ = n ⋅ p ⋅ q 4 0 0 × 1 1 0 × 9 1 0 5 Write the problem in probability notation: P (x x 6 P (x x 7 The corresponding area under the normal curve distribution is shown in the diagram.8 The z x z ( x - μ ) σ ( 3 0 . 5 - 4 0 ) 6 9.5 6 9 The area between z z z 10 The area for z 11 So, the probability that at the most 30 bolts will be defective = 5.67%.Hence the right answer is Option A Click Here To Go Back In triangle DEF, if ∠E = 54o30', d = 21.4, and f = 10.6, then Find ∠D to the neare.. For any parallelogram, find the ratio of sum of the squares of the lengths of the diagonal.. Find the length of AC to two significant digits in the parallelogram ABCD... 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