Question

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Part B) Required Homework Problems Problem 1) A plant manufacturers 12 voltage DC Power Supplies. Two engineers, Kelsier and Dockson, are given access to a batch of 500 power supplies to test. Their tests determine the maximum power that the power supply can provide for a sustained period of time. Kelsie, newly hired quality control engineer randomly selects 10 power supplies from this batch, and his tests results in a sample mean of 150.030 W and the sample standard deviation of 3.502 W Dockson, another quality control engineer has worked for the company for a long time, and knows from past experience that the average capacity of the power supplies that they make is 151 W and sample standard deviation of 4 W Management requires that the maximum power that the DC power supplies can provide should be at least 148 W during sustained use. Assume that the capacity of power supplies is normally distributed. a) How confident is Kelsier that the average maximum power that the average power supply of this batch can provide is at least 148 Watts? b) Based on the data provided by Dockson, estimate the number of power supplies from the given batch that do not satisfy the management requirement. List all your assumptions

Answer 1

Solution (a) Given (u) Sample standard deviation (s) Sample size Sample 150.030 mean 3.502 10 n It is assumed that the capacity of power supply is normally distributed. Then according to the Central limit theorem if the population is nomally distributed then the sample mean is also normally distributed. LetX mean number of watts in a power supply 1 Compute the degree of confidence to which Kelsier is confident that the average maximum power supply for this batch is at least 148 Watts- X-u148-150.030 3.502 P(X2148 P _ S -P(Z 2-1.833) P(Z<1.833) Use the Excel function"=NORMSDIST(1.833)"to compute the probability. fi NORMSDIST(1.833) D P (Z< 1.833)= 0.9666 Therefore, Kelsier is |96.66% confident that the average maximum power supply for this batch is at least 148 Watts. (b)

Given Mean (u 151 Standard deviation (a)4 Let Xnumber of watts in a power supply The probability that a requirements is given by P(X <148) randomly selected power supply does not meet the management Compute the value of above probability- X-и 148-151 Р(X <148) - Р 4 -P(Z <-0.75) to compute the probability Use the Excel function "=NORMSDIST(-0.75) foNORMSDIST(-0.75) D E P (Z< -0.75)= 0.2266 Thus, the probability that a randomly selected power supply does not requirements is 0.2266 meet the management Compute the expected number of power supply in a batch of 500 power supplies that do not meets the management requirements- Е(X) - пхр 500 x0.2266 113.3 s 114 Therefore, from the data provided by Dockson the expected number of power supply in a batch of 500 power supplies that do not meets the management requirements is 114 Assumptions: 1. The sample of 500 power supplies is a simple random sample 2. The population of power supply capacities is normally distributed