Homework 7 Sections 71-74-1 10 of 20 14 The control department of a light buib m

Question

Homework 7 Sections 71-74-1 10 of 20 14 The control department of a light buib manufacturer randomly picks 4400 light bulba fro is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material the sample of 4400 are defective, the m the production lot every week. The records show that, when there used) is 1%, when 1.5% or more of the light bulbs in b. Find the standard deviation of p c. Compute an approximation for Pp 0.015), which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.

Explanation / Answer

(a) Here mean of p^ when there is no malfunction = 0.01

(b) Standard deviation of p^ = sqrt (0.01 * 0.99/4400) = 0.0015

(c) Pr(p^ >= 0.015) = 1 - Pr(p^ < 0.015 ; 0.01; 0.0015)

Z = (0.015 - 0.01)/ 0.0015 = 3.3333

Pr(p^ >= 0.015) = 1 - Pr(p^ < 0.015 ; 0.01; 0.0015) = 1 - Pr(Z < 3.3333) = 1 - 0.999571 = 0.0004

so there is 0.00043 probability that insepctors are called for inspection and repairment even it is working propoery.

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