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Weights of potatoes are normally distributed with a mean of 60 Kilograms and a standard deviation of 12 kilograms. A manager of XYZ supermarket receives a consignment of 10,000 bags of these potatoes.
Required:
i. What is the probability that a random bag will weigh more than 72 kilograms? (3 marks)
ii. What is the probability that a random bag will weigh between 54 kilograms and 78 kilograms? (4 marks)
iii. If any bag, weighing less than 54 kilograms is considered underweight. What are the number of bags that are likely to be declared underweight?
Annual Sales(Rs.000) Frequency
Less than 10 4
Less than 20 20
Less than 30 35
Less than 40 55
Less than 50 62
Less than 60 67
taking 100 and 50 as the assumed average of X and Y respectively.
X 104 111 104 114 118 117 105 108 106 100 104 105
Y 57 55 47 45 45 50 64 63 66 62 69 61
(b) Calculate multiple correlation coefficients R1.23 and R2.13 from the following
information: r13= 0.64, r23 0.79 and r12 0.80
assignment you get is the first easy assignment (i.e. the earlier two were difficult).
Annual Sales(Rs.000) Frequency
Less than 10 4
Less than 20 20
Less than 30 35
Less than 40 55
Less than 50 62
Less than 60 67
8. A box contains 22 balls of which 7 are red, 9 are white, and 6 are black. Four balls are drawn at random from the box without replacement. Find the probability that
(a) three red balls and one white ball are drawn,
(b) the four balls are all red,
(c) the balls are all of the same colour,
(d) there is at least one ball of each colour.
