Question 1.
a) A contractor employs three types of workers -Class A, Class B and Class C. To Class A workers, he pays an average monthly salary of OMR 400, to Class B workers, he pays an average monthly salary of OMR 320 and to Class C workers he pays an average monthly salary of OMR 150. The combined average salary paid by the contractor is OMR 255. If the number of class A and class B worker is 10 each, find the number of class C workers.
b) The standard deviation of Class A, Class B and Class C workers is 15, 7 and 12 respectively. Calculate the coefficient of variation of class A, B and C workers.
c) Comment on the variability in the salaries of the class A, B and C workers.
Question 2. The coefficient of correlation between the age and blood pressure of a sample of 8 persons was found to be + 0.8, the average age is 50 years and average blood pressure is 60. Their standard deviations were 5 and 10 respectively.
a) Obtain the two regression equations
b) Find the expected blood pressure of a person who is 49 years old.
Question 3. The frequency distribution of daily sales for Barka Traders is shown below.
| Daily Sales (OMR) |
Number of days |
|
|
| 100-150 |
2 |
| 150-250 |
16 |
| 250-300 |
12 |
| 300-400 |
25 |
| 400-450 |
12 |
| 450-500 |
15 |
| 500-550 |
12 |
| 550-600 |
6 |
a) Draw a histogram for the above data using the grid given on p.6.
b) Draw less than cumulative frequency curves for the data using the grid below
Use the cumulative frequency graph to estimate the following measures.
Lower Quartile______
Upper Quartile Median_____
20th Percentile_____
Inter Quartile Range______
Number of days the sales is between OMR 350 and OMR 450_____
c) Estimate the mean and standard deviation from the above frequency table (data in question 3) showing all workings.
Question 4. A computer that originally sold for OMR 189 was reduced to sell for OMR139.
i. What is the percentage of reduction in price?
ii. If Mr. Aadil buys 40 of these computers at the reduced price. What is the amount he is going to gain?
b) A portable DVD player which was originally priced at OMR 165, was reduced by 20%
i. Find the reduced price of the DVD player
ii. Find the loss a seller incurs if he buys 100 DVD players at the original price and sells them at the reduced price.
Question 5.
a) The probability that a boy will get a scholarship is 0.9 and that a girl will get a scholarship is 0.8. What is the probability that at least one of them will get the scholarship?
b) Give an example of two events that are
i) Complimentary
ii) Having conditional probabilities
iii) Not independent, but mutually exclusive