Question

Customer feedback indicates that any more than ten defective parts in a box of 250 are unacceptable. Elroy has directed you, the Head of Quality, to determine what probability of any given part being defective (p) is acceptable if we are to have 90% of our customers happy. (Put another way we want the cumulative probability of 10 defects or less to be at least 0.900.) Please answer to three decimal places.

Answer 1

Let p denote the probability of any given part being defective

Let X be the number of defective parts in the box

X can be approximated to Normal distribution with

Mean = 250p

and standard deviation =

The required condition is P(X ≤ 10) ≥ 0.900

-> P(X > 10) ≤ 0.100

Using correction of continuity (Since the discrete distribution is approximated to continuous distribution),

P(X > 10) ≈ P(X > 10.5)

=

Now, corresponding to probability less than 0.100, we have P(Z > 1.2817) = 0.100

Thus,

-> p ≤ 0.0285

Thus, probability of upto 0.029 of any given part being defective is acceptable