Pacific Manufacturing Company has a 2.5 HP industrial pump which, in the recent past, has shown some problems. This has interrupted the production line and has led to unexpected down time of the production line. The maintenance department is considering to take preemptive measures to face this problem. Table 3.a shows the frequency of breakdown of the pump over the past year (52 weeks), which was taken from the companys maintenance records

week	NO . OF BDs	week	NO. OF BDs	week	NO .OF BDs	week	ON .OF BDs	week	ON . OF BDs
1	4	12	2	23	3	34	0	45	4
2	3	13	4	24	1	35	4	46	4
3	0	14	2	25	3	36	1	47	2
4	1	15	1	26	0	37	2	48	0
5	4	16	0	27	0	38	4	49	1
6	3	17	2	28	3	39	0	50	4
7	0	18	3	29	1	40	4	51	4
8	2	19	1	30	1	41	3	52	2
9	0	20	1	31	3	42	2
10	3	21	4	32	2	43	0
11	3	22	4	33	3	44	1

a. From the data given in Table 3.a, prepare a probability distribution table (PDT)

b. Using the random numbers given in Table 3.b, simulate the probable breakdowns of the pump for the coming year (next 52 weeks).

58	37	48	42	30	68	33	11	51	16	85	26	77
90	23	46	84	28	64	63	21	73	17	86	19	18
72	8	59	56	1	35	29	74	22	76	54	36	15
49	62	81	52	41	71	80	13	3	12	88	44	55