Find the solutions for the following system of equations. 5x + 3y = 18 and 2y -2x = -4 and
explain
Solution
Given the system:
5x + 3y = 18 ...........(1)
2y - 2x = -4
We will divide by 2:
==> y - x = -2 .............(2)
Now we will use the substitution method to solve for x and y.
First, we will rewrite equation (2).
==> y = x - 2
Now we will substitute y= x -2 into equation (1).
==> 5x + 3y = 18
==> 5x + 3(x-2) = 18
==> 5x + 3x - 6 = 18
==> 8x = 24
==> x = 24/8 = 3
==> x= 3
Now we to find y, we will substitute into y= x-2
==> y= x- 2 = 3 - 2 = 1
==> y= 1
Then, the solution for the system is the pair ( 3, 1).
Find the standard deviation, for the binomial distribution which has.pdf
1. Find the standard deviation, for the binomial distribution which has the stated values of n and p.
Round your answer to the nearest hundredth.
Problem - n=2815, p=.63
Solution
We know for a binomial distibution with probability function,
P(x = r) = nCr * p^r *(1-p)^(n-r), the mean = np and variance = np(1-p).
Standard deviation, s= (variance)^(1/2) ={np(1-p)}^(1/2).
Standard deviation , s = (np(1-p)}^(1/2)....(1)
So we substitute n = 2815, p = 0.63, in the formula at (1).
Standard deviation = {2815*0.63*(1-0.63)}^(1/2).
Standard deviation = {2815*0.63*0.37}^(1/2) = 25.6159 = 25.62.
So the required standard deviation for the give binomial distribution is 25.62
