The average number of units that the factory workers at Shilo Company assemble p

Question

The average number of units that the factory workers at Shilo Company assemble per week is mu = 45 with a standard deviation of sigma = 12. Assume that the distribution of units assembled is normal. If a sample n = 25 were drawn from all of the workers: What range of units manufactured by this sample would contain the sample mean 90% of the time? What is the probability that the sample mean will be between 40 and 50 units? Is it reasonable for this sample to produce an average of 48 units per week, or is this mean very different from what would be normally expected? How likely is it that this sample will produce more than an average of 55 units?

Explanation / Answer

b) Xbar=45, s=sigma/sqrt n=12/sqrt 25=2.4, compute Z scores for Xi=40 and 50.

Z1=(Xi-Xbar)/s=(40-45)/2.4=-2.08 and Z2=(50-45)/2.4=2.08

P(40<X<50)=0.4812+0.4812=0.2005 (since two Z scores are of different signs, add the probabilities]

c) From information, Xbar=45, mu=48, sigma=12, N=25

Z(Obtained)=(Xbar-mu)/(sigma/sqrt N)=(45-48)/(12/sqrt 25)

=3/2.4=1.25

The p value is 0.2113. The p valu eis not less than alpha=0.05. Therefore, fail to reject null hypothesis. There is not sufficient sample evidence to cocnclude that mean is different from what would be normally expected.

d) P(X>55)=P[Z>(55-45)/2.4]=P(Z>4.16)=0.4999

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