Assignment No. 1

Question 1

The following table shows a summary of marks gained by students in a Statistics examination

        Marks Gained  |  Frequency
        --------------------------
             0-19     |      0
            20-29     |      8
            30-39     |     30
            40-49     |     50
            50-59     |     17
            60-69     |     16
            70-100    |      6

(a) Draw a histogram of these data.
(b) Use the data to estimate the mean and median of the marks.
(c) Give the interquartile range.
(d) Comment upon your findings in parts (a), (b) and (c) above.

Question 2

The following stem-and-leaf plot was obtained from the marks (out of 100) scored by some students sitting for a Math exam.

Stem and leaf plot for Math Scores

 3 | 2589
 4 | 00122234556789999
 5 | 0000001222333344456677788
 6 | 0000011112222344445578
 7 | 1134556

(a) How many students sat for the exam?
(b) Calculate the (arithmetic) mean and the standard deviation for the above marks.
(c) Does a unique mode exist for the above dataset? If so, what is it?
(d) Apply the procedure given on page 44 of Johnson and Bhattacharyya (1996) for finding percentiles.
(e) Draw a boxplot for the above dataset.

Question 3

45% of switches a factory produces are Type A and 55% are Type B. The proportion of faulty switches for Type A is 2% and for Type B is 1.2%.
(a) Calculate the overall proportion of faulty switches.
(b) Given that a faulty switch is selected, what is the probability this will be a switch of Type A?
(c) I buy a switch of each type. What is the probability they are both faulty?
(d) Are the events `I buy a faulty switch of Type A' and `I buy a faulty switch of Type B' (i) mutually exclusive (ii) independent?

Question 4

Hydraulic assemblies for landing gear coming from an aircraft rework facility are inspected for defects. Past history shows that 8% have defects in the shafts alone, 6% have defects in the bushing alone, and 2% have defects in both. If a chosen assembly is to be used on an aircraft, find the probability that it has
(a) a bushing defect;
(b) a shaft or bushing defect;
(c) only one of the two types of defects;
(d) no defects in shafts or bushing.