Decision Science – NMIMS

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NMIMS Global Access

School for Continuing Education (NGA-SCE)

Course: Decision Science

Internal Assignment Applicable for December 2020 Examination

1. The data of two variables X and Y is given below:

TABLE BELOW

Y	X
3	45
4	56
5	54
6	56
7	57
6	58
6	67
6	68
7	76
7	76
8	78
9	79
12	80
13	81
15	84
17	89

a. Calculate the correlation between X and Y

b. Apply the regression between X and Y (as dependent variable)

c. Estimate the R square

d. Predict Y when X = 50

(10 Marks)

Answer 1

A) Calculate the Correlation between X and Y

SUBJECT	Y	X
1	3	45
2	4	56

2. Following ungrouped data of Sales of a company (in millions) is available

52	33	70	95	57	61
57	64	54	94	38	61
50	39	94	63	59	31
68	88	93	48	82	82
74	70	92	76	98	91
32	33	31	75	54	48
36	64	63	66	92	98
36	54	71	86	84	55

91	34	64	67	89	78
97	92	53	56	68	55
93	42	51	77	36	93
44	66	63	33	68	79
83	53	86	76	35	40
55	41	36	39	42	96
60	53	38	51	95	56
48	69	49	33	95	37
83	62	96	34	85	32
39	59	77	62	35	34
54	89	36	45	83	34
39	61	88	86	55	33
69	54	30	38	79	77
95	34	38	91	80	90
88	45	95	71	80	43
61	40	31	61	58	53
91	63	60	94	98	53
50	34	75	74	90	98

a. Make the frequency distribution table with appropiate class interval, frequency,

cumulative frequency.

b. Calculate the mean, median, mode and quartiles of grouped data.

c. Calculate the standard deviation, variance and range

d. Make the following diagrams: Histogram, Frequency Polygon, Ogive

(10 Marks)

Answer 2 a)

52	33	70	95	57	61
57	64	54	94	38	61
50	39	94	63	59	31
68	88	93	48	82	82
74	70	92	76	98	91
32	33	31	75	54	48

3.a. For a certain type of computers, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. Mr Y owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours. (5 Marks

3.b. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last (a) Less than 7 months (b) Between 7 and 12 months (5 Marks)

Answer 3

a)  Mean =50 or µ =50

S.D= 15 or σ=15  

 Probability between 50 < x < 70

Formula

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