Lucca's Italian Sweets. Last year, Lucca's Italian Sweets (LIS) decided to enter the gelato market, and it began cautiously by producing, distributing, and marketing a single flavor—a chocolate-flavored gelato that it calls Choco-yum. The company’s initial venture into the gelato market has been very successful; sales of Choco-yum are higher than expected, and consumers’ ratings of the product have a mean of 80 and a standard deviation of 25 on a 100-point scale, for which 100 is the most favorable score and zero is the least favorable score. Past experience has also shown LIS that a consumer who rates one of its products with a score greater than 75 on this scale will consider purchasing the product, and a score of 75 or less indicates that the consumer will not consider purchasing the product. Emboldened by the success and popularity of its chocolate-flavored gelato, LIS management is now considering the introduction of a second flavor. LIS's marketing department is pressing to extend the product line through the introduction of a vanilla-flavored gelato that would be called Vani-yum, but senior managers are concerned about whether or not Vani-yum will increase LIS's market share by appealing to potential customers who do not like Choco-yum. That is, the goal in offering the new product is to increase LIS's market share rather than cannibalize existing sales of Choco-yum. The marketing department has proposed giving tastes of both Choco-yum and Vani-yum to a simple random sample of 50 customers and asking each of them to rate the two gelatos on the 100-point scale. If the mean score given to Choco-yum by this sample of consumers is 75 or less, LIS's senior management believes the sample can be used to assess whether Vani-yum will appeal to potential customers who do not like Choco-yum. Prepare a report that addresses the following: a. Calculate the probability that the mean score of Choco-yum given by the simple random sample of LIS customers will be 75 or less. b. If the Marketing Department increases the sample size to 150, what is the probability that the mean score of Choco-yum given by the simple random sample of LIS customers will be 75 or less? c. Explain to LIS senior management why the probability that the mean score of Choco-yum given by the simple random sample of LIS customers will be 75 or less is different for these two sample sizes.
For this problem I had 7.93% for the
im also confused as the difference for vanilla and chocolate propositions in the question. Do I need to figured out the vanilla probability?
Does it
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Lucca's Italian Sweets. Last year, Lucca's Italian Sweets (LIS) decided to enter the gelato market, and it began cautiously by producing, distributing, and marketing a single flavor—a chocolate-flavored gelato that it calls Choco-yum. The company’s initial venture into the gelato market has been very successful; sales of Choco-yum are higher than expected, and consumers’ ratings of the product have a mean of 80 and a standard deviation of 25 on a 100-point scale, for which 100 is the most favorable score and zero is the least favorable score. Past experience has also shown LIS that a consumer who rates one of its products with a score greater than 75 on this scale will consider purchasing the product, and a score of 75 or less indicates that the consumer will not consider purchasing the product.
Emboldened by the success and popularity of its chocolate-flavored gelato, LIS management is now considering the introduction of a second flavor. LIS's marketing department is pressing to extend the product line through the introduction of a vanilla-flavored gelato that would be called Vani-yum, but senior managers are concerned about whether or not Vani-yum will increase LIS's market share by appealing to potential customers who do not like Choco-yum. That is, the goal in offering the new product is to increase LIS's market share rather than cannibalize existing sales of Choco-yum. The marketing department has proposed giving tastes of both Choco-yum and Vani-yum to a simple random sample of 50 customers and asking each of them to rate the two gelatos on the 100-point scale. If the mean score given to Choco-yum by this sample of consumers is 75 or less, LIS's senior management believes the sample can be used to assess whether Vani-yum will appeal to potential customers who do not like Choco-yum.
Prepare a report that addresses the following:
a. Calculate the probability that the mean score of Choco-yum given by the simple random sample of LIS customers will be 75 or less.
b. If the Marketing Department increases the sample size to 150, what is the probability that the mean score of Choco-yum given by the simple random sample of LIS customers will be 75 or less?
c. Explain to LIS senior management why the probability that the mean score of Choco-yum given by the simple random sample of LIS customers will be 75 or less is different for these two sample sizes.
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