Question

2% of widgets manufactured by Acme Gadget Co. are defective. a) if 20 Acme widgets are selected at random, what is the probability of getting at least 1 that is defective. B) Find the probability at least 3 widgets need to be selected to find 1 that is defective. C) what is the expected number of widgets that need to be inspected to find one that is defective?

Answer 1

Part a)

P ( X >= 1 ) = 1 - P ( X = 0 )

P ( X >= 1 ) = 0.3324

Part b)

P ( X >= 3 ) = 1 - P ( X <= 2 )

P ( X >= 3 ) = 1 - 0.0071

Part c)

Mean = n * P = ( 20 * 0.02 ) = 0.4
Variance = n * P * Q = ( 20 * 0.02 * 0.98 ) = 0.392
Standard deviation = = 0.6261