Question

The quality control director of a small company that manufactures exercise equipment knows that 10% 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. (hint: write down what you know from the problem) a) Describe the sampling distribution of P, the proportion of the 600 units that will be returned for service. b) What is the probability that more than 3% of the 600 units will be returned for service? c) What is the probability that more than 5% of the 600 units will be returned for service? d) Would it be unusual if in a random sample of 600 units, 5% were returned for service? Explain your answer.

Answer 1

the quality control director of a small company that manufactures exercise equipment knows that 10% of their products are defective.

The Quality control disector of a small company that Manufactuses exercise equipment knows that 64% of their Products are defectives Solutions ; will be detyoned pooportion of units that population Service tos p . 3% - 0.03. Sample Size = n - 600 standard Eroos of the point estimate = op Op - Price 0.03% (1 -0.03) GOO - 0.0070. (a) Describe the sampling din toibution of the 600 units that will be retooned for the proportion of service? solution : of foo units that will be returned Sample proportion Sonice -

Mean of the sampling distribution = p = 0.03 stondard corons of the sampling diatói bution - 5 = 0.0070 b) what is the poobability that more than 3% of the col units till be setunned for Honvice? solution ; units will be Probability that more than 3% of the se long as 'Convice - P( 2 0.03) Test Statistici 2= ŷ - P → z = 0.03 -0.03 0.0070 Hence, P(820.03) = P(zzo) From nome distribution table ; P(270) = 6.50 Hence probability that mose than 3% of the 600 units will be Betunned for service - 0.50

the GoG c. what is the probability that more than 5% of units will be returned for service? solution: Probability that more than 50% of the 600 units will be the turned for service - PIÑO 30.05) Test Statistics - z= PP > 2 = 0.05 -0-03 0.0070 - 2.872 Hence IP(P >0.05) = P(2> 9.872) foom = 0.0020. nomal distoibution table; P(Z > 9.872) d) would it be unusal if in a random sample of 600 units 50% were detuonent for service? Explain your answell? solution Since the above lue is less than 0.05, hence it would unusual that 50j of the 600 units will be selurned 100 novice