Conveyor Belt Motors (20 points) The brushes in the motors that control the conveyor belts at Delectable Delights need to be rep
laced periodically. Since there are many conveyor belts through the buildings, a supply of brushes is always kept on hand. The brushes come in shipments of 1000 from a supplier who claims that no more than 2% will be defective. Out of each shipment, a random sample of 10 brushes is selected for testing. If there are any defective brushes in the sample, the shipment will be rejected. Let X be the number of defective brushes in a sample of size 10. (a) Could the random variable X be considered a Binomial random variable? Justify your answer using the properties of a Binomial random variable from page 88 in the lecture guide. (5 points) (b) Regardless of your answer in part (a), assume that X is a Binomial random variable. Write out the sample space for X. What are the values of the parameters n and p? (5 points) (c) Calculate the mean and standard deviation for X. Show your calculations and round your answers to two decimal places if necessary. (5 points) (d) Calculate the probability that a shipment will be rejected. Show your work by substituting values into the appropriate formula. Include probability notation in your answer. (5 points)
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