Last year Marion Dairies decided to enter the yogurt market, and it began cautiously byproducing, distributing, and marketing a single flavor - a blueberry-flavored yogurt that it callsBlugert. The company' initial venture into the yogurt market has been very successful; sales ofBlugert are higher than expected, and consumers' ratings of the product have a mean of 80 anda standard deviation of 25 on a 100-point scale for which 100 is the most favorable score andzero is the least favorable score. Past experience has also shown Marion Dairies that aconsumer who rates one of its products with a score greater than 75 on this scale will considerpurchasing the product, and a score of 75 or less indicates that the consumer will not considerpurchasing the product.Emboldened by the success and popularity of its blueberry-flavored yogurt, Marion Dairiesmanagement is now considering the introduction of a second flavor. Marion's marketingdepartment is pressing to extend the product line through the introduction of a strawberryflavoredyogurt that would be called Strawgurt, but senior managers are concerned aboutwhether or not Strawgurt will increase Marion's market share by appealing to potentialcustomers who do not like Blugert. That is, the goal in offering the new product is to increasethe market share rather than cannibalize existing sales of Blugert. The marketing departmenthas proposed giving tastes of both Blugert and Strawgurt to a simple random sample of 50customers and asking each of them to rate the two yogurts on the 100-point scale. If the meanscore given to Blugert by this sample of consumers is 75 or less, Marion's senior managementbelieves the sample can be used to assess whether Strawgurt will appeal to potential customerswho do not like Blugert.1. Calculate the probability that the mean score of Blugert given by the simple randomsample of Marion Dairies customers will be 75 or less.2. If the Marketing Department increases the sample size to 150, what is the probabilitythat the mean score of Blugert given by the simple random sample of Marion Dairiescustomers will be 75 or less?3. Explain to Marion Dairies senior management why the probability that the mean scoreof Blugert given by the simple random sample of Marion Dairies customers will be 75 orless differs for these two sample sizes.
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