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Honeydew bottles honey jars and sells them through retail channels. The weight on the sticker says 20 oz and Honeydew claims its bottles have a weight that is normally distributed with a mean of 20 oz and std dev of 2 oz. The retailer has been receiving several complaints lately and decides to measure a sample of 4 jars and finds weights of 18, 20, 17 and 19 oz respectively.
a. The retailer complains to Honeydew if he is 95% confident that the mean is lower than advertised. Does he complain?
b. If the retailer’s customers return any jar under 18 oz in weight, what fraction of the retailer’s sales result in a return?
c. Assuming Honeydew’s claim is true, what is their current sigma capability? What can they do to reduce the fraction of returns to 5%? What then would the new sigma capability be?
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