The breaking strength of 80 "test pieces" of a certain alloy is given in the following table, the unit being given to the nearest thousand grams per square inch.

Breaking strength Number of pieces

44-46 3

4648 24

4850 27

5052 21

5254 5

(i) Calculate the average breaking strength

(ii) Calculate the standard deviation of the breaking strength.

(iii) Calculate the percentage of observations lying between two standard deviations of the mean.

QUESTION TWO

A. A survey of 200 retail grocery shops revealed the following monthly income pattern:

Monthly Income Number of shops

Under k20,000 102

K20,000 to k30,000 61

k30,000 and above 37

(i) What is the probability that a particular shop has a monthly income under k20,000?

(ii) What is the probability that a selected shop at random has either an income between k20,000 and k30,000 or an income of k30,000 and more?

B. From a computer tally based on employer records, the personnel manager of a large manufacturing firm finds that 15% of the firm's employees are supervisors and 25% of the firm's employees are college graduates. He also discovers that 5% are both supervisors and college graduates. Suppose an employee is selected at random from the personnel records, what is a probability of

(i) selecting a person who is both a college graduate and supervisor?

(ii) selecting a person who is neither a supervisor nor a college graduate?

C. The probability that a new marketing approach will be successful is 0.6. The probability that the expenditure for developing the approach can be kept within the original budget is 0.50. The probability that both of these will be achieved is 0.30.

(i) What is the probability that at least one of the objectives will be achieved?

(ii) For the two events described above, determine whether the events are independent or dependent.

D. A man wants to marry a girl having the following qualities: Beautifulthe probability of getting such a girl is one in twenty; has a well paying jobthe probability of getting this one is one in fifty; respectful--the probability here is one in hundred. Find the probability of him getting married to such a girl when the possession of these three attributes is independent.

E. A manufacturing firm produces pipes in two plants I and II with daily production of 1,500 and 2000 pipes, respectively. The fraction of defective pipes produced by plants I and II are 0.006 and 0.008, respectively. If a pipe is selected at random from that day's production is found to be defective, what is the probability that it came from plant I or plant II?