Question

1) In economics, of all new products put on the market, only 5% become popular and last more than five years on the market. using normal approximation for this binomial distribution, if a store introduces 200 new product. what is the probability that at most 12 products last more than five years on the market? Round to four decimal places.

2) In economics, of all new products put on the market, 90% fail and are taken off the market within two years. using normal approximation for this binomial distribution, if a store introduces 90 new products. what is the probability that within two years at most 75 fail using correction for continuity? Round to four decimal places.

Answer 1

1) n = 200

p = 0.05

= np = 200 * 0.05 = 10

= sqrt(np(1 - p))

= sqrt(200 * 0.05 * (1 - 0.05))

= 3.0822

P(X < 12)

= P((X - )/< (12.5 - )/)

= P(Z < (12.5 - 10)/3.0822)

= P(Z < 0.81)

= 0.7910

2) n = 90

p = 0.9

= np = 90 * 0.9 = 81

= sqrt(np(1 - p))

= sqrt(90 * 0.9 * 0.1)

= 2.846

P(X < 75)

= P((X - )/< (75.5 - )/)

= P(Z < (75.5 - 81)/2.846)

= P(Z < -1.93)

= 0.0268