The number of wiring packages that can be assembled by a company\'s employees ha

Question

The number of wiring packages that can be assembled by a company's employees has a normal distribution, with a mean equal to 17.9 per hour and a standard deviation of 1.2 per hour. (a) What are the mean and standard deviation of the number X of packages produced per worker in an 8-hour day? (Round your standard deviation to three decimal places.) mean ________ standard deviation ____________ (b) Do you expect the probability distribution for X to be mound-shaped and approximately normal? Explain. Yes, since the standard deviation is less than 3, the sampling distribution of the sum will be approximately normal. Yes, since the original population is normal, the sampling distribution of the sum will also be approximately normal. No, since the original population is not normal, the sampling distribution of the sum will not be approximately normal. No, since the original population ?s normal, the sampling distribution of the sum cannot be normal. No, since the standard deviation is more than 3, the sampling distribution of the sum will not be approximately normal. (c) What is the probability that a worker will produce at least 146 packages per 8-hour day? (Round your answer to four decimal places.)

Explanation / Answer

a)

mean = 8*17.9 = 143.2

SD=8*1.2 = 9.6

c)

z value for 146, z=(146-143.2)/9.6 =0.29

P( x>=146) = P(z >=0.29) = 0.3859

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