Question

Two years ago “Illyria” decided to enter the chocolate market, and it began by producing vanilla flavored chocolate called “Vanchoc”. The company’s sales of chocolate are higher than expected, and consumers’ ratings of the product have a mean of 75 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 Illyria that a consumer who rates one of its products with a score greater than 70 on this scale will consider purchasing the product, and a score of 70 or less indicates that the consumer will not consider purchasing the product. Encouraged by these results, Illyria is now considering the introduction of a second flavor, a strawberry flavored chocolate that would be called “Strawchoc”, but managers are concerned about whether or not Strawchoc will increase Illyrias’s market share by appealing to potential customers who do not like Vanchoc. That is, the goal in offering the new product is to increase the market share rather than cannibalize existing sales of Vanchoc. The marketing department has proposed giving tastes of both Vanchoc and Strawchoc to a simple random sample of 50 customers and asking each of them to rate the two chocolates on the 100-point scale. If the mean score given to Vanchoc by this sample of consumers is 70 or less, Illyria’s senior management believes the sample can be used to assess whether Strawchoc will appeal to potential customers who do not like Vanchoc.

1. Calculate the probability that the mean score of Vanchoc given by the simple random sample of Illyria’s customers will be 70 or less. (10 pts)

2. If the marketing department increases the sample size to 150, what is the probability that the mean score of Vanchoc given by the simple random sample of Illyria’s customers will be 70 or less? (10 pts)

3. Explain to Illyria’s management why the probability that the mean score of Vanchoc given by the simple random sample of Illyria’s customers will be 70 or less differs for these two sample sizes.

Answer 1

answered by: anonymous