The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.5% or more are defective, they call repair technicians for service.The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p . (b)Find the standard deviation of p. (c)Compute an approximation for P(z≥0.015), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.
The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.5% or more are defective, they call repair technicians for service.The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p . (b)Find the standard deviation of p. (c)Compute an approximation for P(z≥0.015), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.5% or more are defective, they call repair technicians for service.The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly.
Answer the following. (If necessary, consult a list of formulas.)
|
(a)Find the mean of p
. (b)Find the standard deviation of p.
(c)Compute an approximation for
P(z≥0.015), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.
|
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