1. The following data were collected on scores (out of a possible 100) for a pretest in quantity methods. Using Excel's statistical functions complete the following questions.
(a) What are the means for the two data sets?
(b) What are the medians for the two data sets? Is there a difference or similarity between the mean and the median? Explain the similarity or difference.
(c) What are the standard deviations for each of the data sets?
(d) Construct a histogram for each data se, using 5 as your class with and starting with 60 as your lowest class for data set 1 and 10 for data set 2.
(e) Relate the standard deviation you calculated in part c to your histograms in part d.
(f) Based on problem 8, which data set is more stable. Base your answer on standard deviation values. Compare both frequency histograms and which shows a normal distribution behavior?
2. Easter Airlines knows that 20% of its customers fly first class, 20% fly business class, and the rest fly coach. Of those customers who fly first class, 70% are from the East Coast while 30% are from elsewhere. In addition, of those customers who fly business class, 50% are from the East Coast and 50% are from elsewhere. Finally, of those customers that fly coach class, 75% are from elsewhere and 25% are from the East Coast.
(a) Construct a probability tree for this problem.
(b) Construct a probability table for this problem.
(c) Determine the probability that a customer from East Cost will fly first class.
(d) What is the probability that a customer will be from the East Coast?
(e) Based on problem 11, if you are the owner of the Eastern airlines how many seats do you need to cover the East Coast flights with a monthly total demand of 487,000 people for the entire airline?
If the airplane has 200 seats, how you will distribute them by first class, business class and coach?
(f) Determine how these problems will support your decision making process?