problem 1: The given table provides scores and sales are nine salesmen during last one year in a certain firm:
Text scores 14 19 24 21 26 22 15 20 19
Sales (in 000'Rupees) 31 36 48 37 50 45 33 41 39
find out the Karl Pearson's Coefficient of Correlation and interpret the result.
x y d_{x} = x-20 dy = y-40 d_{x}d_{y} dx^{2} dy^{2}
14 31 -6 -9 54 36 81
19 36 -1 -4 4 1 16
24 48 4 8 32 16 64
21 37 1 -3 3 1 9
26 50 6 10 60 36 100
22 45 2 5 10 4 25
15 33 -5 -7 35 25 49
20 41 0 1 0 0 1
19 39 -1 -1 1 1 1
Σx = 180 Σy = 180 Σdxdy = 93 Σdx^{2} = 120 Σdy^{2} = 346
problem 2: Find out the probability of drawing a diamond card in each of consecutive draws from a well shuffled pack of cards, if the card drawn is not replaced after the first draw.
problem 3: A bag contains 5 white, 7 red and 8 black balls. If four balls are drawn one by one without replacement, find out the probability of getting all the white balls.