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(MATH144)07F-Revision question.pdf
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Question 1
In a marketing survey, ABC Co. Ltd. takes a random sample of its retail outlets. The sales of the outlets in a certain month were as follows:
Sales (hundred thousand)
Class mark, x
Number of outlets, f
0 C less than 2
1
2
2 C less than 4
3
5
4 C less than 6
5
11
6 C less than 8
7
16
8 C less than 10
9
12
10 C less than 12
11
5
12 C less than 14
13
2
(a)
Calculate the mean, standard deviation and coefficient of variation of the monthly sales.
(8marks)
(b)
Calculate, from the above table, the monthly sales exceeded by 20% of the sample.
(4 marks)
(c)
The company prepares to distribute a new product through outlets having monthly sales more than or equal to $880,000. Estimate, from the above table, the probability that a retail outlet will be offered this new product.
(4 marks)
(d)
The retail outlets of a rival company, XYZ Co. Ltd., had a mean monthly sales of $550,000 and a standard deviation of $160,000 in the same month. Which company (ABC or XYZ) had a greater variability in monthly sales?
(4 marks)
Question 2
(a)
A city education authority carried out a survey of the IQ scores of the children in its school at all ages. The distribution of the IQ scores was found to be normal with mean of 100; and 1.7% of the children were found to have IQ score less than 70.
(i)
Calculate the standard deviation of the IQ scores.
(3 marks)
(ii)
What is the probability that a randomly selected child will have IQ score more than 115?
(2 marks)
(b)
A fashion designer has recently designed a new dress. The probability that the new dress will get an award for its design is 0.26, the probability that it will get an award for the efficient use of materials is 0.22, and the probability that it will get both awards is 0.11.
(i)
What is the probability that the dress will get at least one of the two awards?
(3 marks)
(ii)
Given that the dress gets the awards for its design, what is the probability that it will get the award for efficient use of materials?
(3 marks)
(iii)
Given that the dress does not get the award for its design, what is the probability that it will not get the award for the efficient use of materials?
(4 marks)
(c)
A large manufacturing firm purchases a certain component from three different vendors A, B and C. Vendor A supplies 40% of the components and has a defective rate of 2%, vendor B supplies 40% of the components and has a defective rate of 1% and vendor C supplies the remainder of the components and has a defective rate of 3%. If one component is randomly selected from a shipment and is found defective, what i