Initially a box contains 3 balls identical in all aspects except for their colour, each of...

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Initially a box contains 3 balls identical in all aspects except for their colour, each of which is either white or black. Now, one white ball identical to balls in the box in all aspects except for its colour, is added into the box and then one ball is drawn at random from the box. Assuming that the four possible initial compositions of the balls in the box are equally likely, find the probability that (i) the ball drawn is white, and (ii) initially there were exactly 2 black balls in the box, given that the ball drawn is white. (b) Let the mean and the standard deviation of the set of values {i=1,2,...,n} be and o respectively. Find the mean and the standard deviation of the set of values {ax : i=1,2,..., n}, where a is a constant. Monthly salaries of 50 employees at a certain company are summarised in the following table: Monthly Salary (in thousand rupees) 5-15 15-25 25- 35 35 - 45 45-55 Number of Employees 9 11 14 10 6 Estimate the mean and the standard deviation of the monthly salaries of the 50 employees. At the beginning of a year, the monthly salary of each employee is increased by p%. It is given that the mean of the new monthly salaries of the above 50 employees is 29 172 rupees. Estimate the value of p and the standard deviation of the new monthly salaries of the 50 employees. Initially a box contains 3 balls identical in all aspects except for their colour, each of which is either white or black. Now, one white ball identical to balls in the box in all aspects except for its colour, is added into the box and then one ball is drawn at random from the box. Assuming that the four possible initial compositions of the balls in the box are equally likely, find the probability that (i) the ball drawn is white, and (ii) initially there were exactly 2 black balls in the box, given that the ball drawn is white. (b) Let the mean and the standard deviation of the set of values {i=1,2,...,n} be and o respectively. Find the mean and the standard deviation of the set of values {ax : i=1,2,..., n}, where a is a constant. Monthly salaries of 50 employees at a certain company are summarised in the following table: Monthly Salary (in thousand rupees) 5-15 15-25 25- 35 35 - 45 45-55 Number of Employees 9 11 14 10 6 Estimate the mean and the standard deviation of the monthly salaries of the 50 employees. At the beginning of a year, the monthly salary of each employee is increased by p%. It is given that the mean of the new monthly salaries of the above 50 employees is 29 172 rupees. Estimate the value of p and the standard deviation of the new monthly salaries of the 50 employees.

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