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(ISMT111)Mid03.pdf
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ISMT111 Business Statistics
Mid-Term Examination

17th October 2003
Directions 1) Answer ALL SIX questions. Marks are shown in square brackets. 2) There are 4 pages in this examination paper. Check to make sure you have a complete set and notify the invigilator immediately if part of it is missing. 3) Key formulas and statistical tables are provided separately. 4) Calculator may be used in this examination. 5) You are given TWO HOURS to complete this examination. Do not begin until you are told to do so.
Question 1: [16 Marks]
The following table gives the revenue change (in percentage) of 10 companies in 2002:
3.4 -4.8 2.1 4.3 13.8 1.5 -2.4 -5.7 1.1 -0.6
(a)
What are the sample mean, standard deviation and interquartile range of the revenue change?

(b)
Is there any extreme value in the sample?

(c)
Suggest and calculate a suitable location measure for the revenue change. Explain your answer.

(d)
Suppose we have another sample of five revenue changes whose mean and standard deviation are 1.2 and 4.78 respectively. Calculate the combined standard deviation of the fifteen observations.


Question 2: [18 Marks]
A company receives a shipment of twenty items. Because inspection of each individual item is expensive, it has a policy of checking a random sample of six items for such a shipment, accepting delivery if no more than one sampled item is defective. Suppose there are five defective items in a specific shipment and the random sample is chosen without replacements from that shipment.
(a)
What is the expected number of defective items in the sample?

(b)
What is the probability that the specific shipment is accepted?

(c)
Suppose the first item of the sample was found to be defective. What is the probability that the specific shipment is accepted?

(d)
Suppose there is one defective item in the first four items of the sample. What is the probability that the specific shipment is accepted?


Question 3: [16 Marks]
A record store owner assesses customers entering the store as high school age, university age, or older, and finds 30%, 50%, and 20% respectively of all customers fall into these categories. The owner also found that purchases were made by 20% of high school age customers, by 60% of college age customers, and by 80% of older customers.
(a)
What is the probability that a randomly chosen customer entering the store will make a purchase?

(b)
If a randomly chosen customer makes a purchase, what is the probability that this customer is high school age?

(c)
If a randomly chosen customer DOES NOT make a purchase, what is the probability that this customer is NOT high school age?



Question 4: [14 Marks]
Jerry, owner of Jerrys Pizza, has a difficult decision on his hands. He has found that the number of his famous Jerrys Supreme pizzas that he sells has the following probability distribution:

Since the preparation time for each pizza is length