HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.

Two lines of regression are 10x + 3y − 62 = 0 and 6x + 5y − 50 = 0. Identify the regression of x on y. Hence find `bar x, bar y` and r.

For certain X and Y series, which are correlated the two lines of regression are 10y = 3x + 170 and 5x + 70 = 6y. Find the correlation coefficient between them. Find the mean values of X and Y.

Regression equations of two series are 2x − y − 15 = 0 and 3x − 4y + 25 = 0. Find `bar x, bar y` and regression coefficients. Also find coefficients of correlation. [Given `sqrt0.375` = 0.61]

The two regression lines between height (X) in inches and weight (Y) in kgs of girls are,
4y − 15x + 500 = 0
and 20x − 3y − 900 = 0
Find the mean height and weight of the group. Also, estimate the weight of a girl whose height is 70 inches.

Find the line of regression of X on Y for the following data:

n = 8, `sum(x_i - bar x)^2 = 36, sum(y_i - bar y)^2 = 44, sum(x_i - bar x)(y_i - bar y) = 24`

The following results were obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.

and `sum (x_i - bar x)(y_i - bar y) = 1120`. Find the prediction of blood pressure of a man of age 40 years.

The equations of two regression lines are 10x − 4y = 80 and 10y − 9x = − 40 Find:

1. `bar x and bar y`
2. b_YX and b_XY
3. If var (Y) = 36, obtain var (X)
4. r

If b_YX = − 0.6 and b_XY = − 0.216, then find correlation coefficient between X and Y. Comment on it.

The Cost of Living Index Number for years 1995 and 1999 are 140 and 200 respectively. A person earns ₹ 11,200 per month in the year 1995. What should be his monthly earnings in the year 1999 in order to maintain his standard of living as in the year 1995?

Solve the following problem :

Calculate the cost of living number for the following data.

Solve the following problem :

The cost of living index number for year 2000 and 2003 are 150 and 210 respectively. A person earns ₹ 13,500 per month in the year 2000. What should be his monthly earning in the year 2003 in order to maintain the same standard of living?

Find the optimal sequence that minimizes total time required to complete the following jobs in the order ABC. The processing times are given in hrs.

A publisher produces 5 books on Mathematics. The books have to go through composing, printing and binding done by 3 machines P, Q, R. The time schedule for the entire task in proper unit is as follows.

Determine the optimum time required to finish the entire task.

In sequencing, an optimal path is one that minimizes _______.

If jobs A to D have processing times as 5, 6, 8, 4 on first machine and 4, 7, 9, 10 on second machine then the optimal sequence is ______.

Solve the following problem :

Consider the problem of assigning five operators to five machines. The assignment costs are given in following table.

Operator A cannot be assigned to machine 3 and operator C cannot be assigned to machine 4. Find the optimal assignment schedule.

Solve the following problem :

A chartered accountant’s firm has accepted five new cases. The estimated number of days required by each of their five employees for each case are given below, where - means that the particular employee cannot be assigned the particular case. Determine the optimal assignment of cases of the employees so that the total number of days required to complete these five cases will be minimum. Also find the minimum number of days.

Choose the correct alternative:

If for a bivariate data, b_YX = – 1.2 and b_XY = – 0.3, then r = ______

Choose the correct alternative:

If the regression equation X on Y is 3x + 2y = 26, then b_xy equal to