Question

a) The following table shows, for a group of 12 production workers, the number of months of working experience on a particular process each of them had, and the number of defective items that they produced during a given week.

Worker	A	B	C	D	E	F	G	H	I	J	K	L
Experience(Months)	9	11	8	16	10	14	12	6	4	13	3	11
Number of rejects produced	24	18	26	14	21	16	22	24	36	20	30	23

You are required to:

I) calculate the coefficient of linear correlation for the data, and comment on the result.                                                                                                          [8 marks]

ii) Determine the coefficient of determination for the data, and explain its implication.

                                                                                                                    [4 marks]

iii) Determine the equation of the least squares regression line, and comments on the values of the coefficient and the constant.                                           [8 marks]

b) The quality controller of a soft drinks producing company estimates the probability of rejects as 10% on a monthly basis. If she randomly selects a sample of 10 packets find the probability that:

I) All are non – defective                                                                   [2 marks]

ii) Exactly 2 are defective                                                                  [2 marks]

iii) At most 8 are defective                                                                 [3 marks]

iv) At least 2 are defective                                                                 [3 marks]

v) Between 2 and 4 (inclusive) are defective.                                    [4 marks]

b) The quality controller of a soft drinks producing company estimates the probability of rejects as 10% on a monthly basis. If she randomly selects a sample of 10 packets find the probability that:

I) All are non – defective                                                                   [2 marks]

ii) Exactly 2 are defective                                                                  [2 marks]

iii) At most 8 are defective                                                                 [3 marks]

iv) At least 2 are defective                                                                 [3 marks]

v) Between 2 and 4 (inclusive) are defective.                                    

Answer 1

a)

I)

The correlation coefficient is obtained in excel using the function =CORREL(). the screenshot is shown below,

The correlation coefficient value is -0.9036 which indicates that there is a strong negative correlation between Experience and Number of rejects produced such that as the experience increases, the number of rejects produced decreases

II)

The Coefficient of determination is obtained in excel using the function =RSQ(). The screenshot is shown below,

The R square value defines how well the variance of one variable is explained by the other. The R square value is 0.8166 which means the experience explained 81.66% of the variance of number of rejects produced

III)

The least squares regression line is defined as,

Where, a = intercept and b = slope

Y represents number of rejects produced and represents experience in months

The least squares estimate of slope and intercept are obtained in excel. The screenshot is shown below,

b)

The sample size of 10 packets will have a binomial distribution with parameter n and p. The distribution can be represented as;

For calculation purpose, the probabilities are obtained in excel. The screenshot is shown below,