BUSINESS MATHEMATICS AND STATISTICS (MBA-5528)

BUSINESS MATHEMATICS AND STATISTICS (MBA-5528)

ASSIGNMENT No. 1

Q. 1  (a)     A data processing manager purchased remote terminal processing time to run special jobs at two different computer “utilities”. She wishes to sign a long-term contract with the firm whose computer causes the least delay on the average. The numbers of minutes of delayed processing per week were obtained during trial periods with each firm and are provided below:

                  Compu Quick     210     15      47      93       104

                  Dial-a-Pute 18     341    523     25      19       293      115      203

Assuming that trial experience is representative of future performance, which firm should receive the business? Substantiate your answer with appropriate calculations.      (10)

(b)         The length of life of 220 incandescent 60-watt lamps was obtained and yielded the frequency distribution shown in the table given below:                                                                

Class Limit	Frequency
500-599	3
600-699	7
700-799	14
800-899	28
900-999	64
1000-1099	57
1100-1199	23
1200-1299	13
1300-1399	7
1400-1499	4

1.            Construct a histogram of these data, using a vertical scale for relative frequencies.

2.            Find the mean length of life

3.            Find the standard deviation                                                       (10)

Q. 2  (a)     A hard working student has 90 percent chance to pass the examination and that pass percentage of the university is 28 percent. Suppose 20% students work hard. What is the probability that a person who has passed has really worked hard?

         (b)     A sales person has 10 percent chance of making a sale to any customer who is called upon. If 20 calls are made, what is the chance that (i) fewer than three sales are made (ii) At least one sale is made (iii) More than five are made?                                                                             (20)

Q. 3   (a)    The wrist circumference of adult males is normally distributed with a mean of m = 6.85² and a standard deviation of s = 0.40². One man is selected at random. Determine the probabilities for the following possible wrist sizes.

                  1.   Less than 8.00²

                  2.   Between 5.75² and 6.75²

 (b)   The achievement scores for a college entrance examination are normally distributed with a mean of 75 and a standard deviation of 10. What fraction of the scores would you expect to lie between 70 and 90?      (20)

Q. 4   The shopping times were recorded for 64 randomly selected customers for a local supermarket. The average and variance of the 64 shopping times were 33 minutes and 256, respectively. Estimate the true average shopping time per customer, with a confidence coefficient of 1–a = 0.90.                (20)

Q. 5   A vice-president for a large corporation claims that salesmen are averaging no more than 15 sales contacts per week. (She would like to increase this figure) As check on her claim, 36 salesmen are selected at random, and the number of contacts is recorded for a single randomly selected week. The sample reveals a mean of 17 contacts and a variance of 9. Does the evidence contradict the vice-president’s claim?

          Use a = 0.50.                                                                                             (20)