Question

(Normal Approximation) A process yields 2% defective items. Suppose 2500 items are randomly selected from the process. Use the normal curve approximation (with half-unit correction) to find the probability that the number of defectives exceeds 55?

Answer 1

Mean = n * P = 2500 * 0.02 = 50

Standard deviation =

Using Normal approximation to Binomial distribution

P ( X > 55 )

Using continuity correction

P ( X > 55 ) = P ( X > 55 + 0.5 ) = P ( X > 55.5 )

P ( X > 55.5 ) = 1 - P ( X < 55.5 )
Standardizing the value

Z = ( 55.5 - 50 ) / 7
Z = 0.79

P ( Z > 0.79 )
P ( X > 55.5 ) = 1 - P ( Z < 0.79 )
P ( X > 55.5 ) = 1 - 0.7852
P ( X > 55.5 ) = 0.2148

P ( X > 55 ) = 0.2148