the quality control director of a small company that manufactures exercise equip

Question

the quality control director of a small company that manufactures exercise equipment knows that10% of their products are defective. market research shows that only 30% of their customers will use the product in the first year after the sale. So, the manufacturer expects that 3% of the units will be returned for service under a one year full warranty. This company expects to sell 600 units next year. For this problem, assume the next years production can be considered a simple random sample of all the units produced.

A. describe (Mean, standard deviation and shape) the sampling of ^p, the proportion of the 600 units that will be returned for service

b. what is the probability that more than 2.75% of the 600 units will be returned for service

c. what is the probability that between 2% and 4% of the 600 units will be returned for service?

Explanation / Answer

a) Mean of the sampling of p phat =3%

std error =(phat*(1-phat)/n)1/2 =0.6964%

for np =0.03*600=18 and n(1-p)=582 both are greater then 10 therfore shape will be approximately normal

b)  probability that more than 2.75% of the 600 units will be returned for service =P(X>2.75)

=1-P(X<2.75)=1-P(Z<(2.75-3)/0.6964)=1-P(Z<-0.3590)=1-0.3598=0.6402

c)

P(2<X<4) =P((2-3)/0.6964<Z<(4-3)/0.6964)=P(-1.4359<Z<1.4359)=0.9245-0.0755=0.8490

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