11x10=110
110+40=150
150/6=25
25-8=17
17 is the number.
Ok so the average is 50
average of x number of things is
(add value of all things)/x=average
4 test scores needed
so divide by 4
3 test scores ar known
average is 50
x= missing score
(43+48+42+x)/4=50
times 4 both sides
133+x=200
minus 133 both sides
x=67
a score of 67 is needed
Answer:
![E(X) = \sum_{i=1}^n X_i P(X_i) = 0*0.031 +1*0.156+ 2*0.313+3*0.313+ 4*0.156+ 5*0.031 = 2.5](https://tex.z-dn.net/?f=%20E%28X%29%20%3D%20%5Csum_%7Bi%3D1%7D%5En%20X_i%20P%28X_i%29%20%3D%200%2A0.031%20%2B1%2A0.156%2B%202%2A0.313%2B3%2A0.313%2B%204%2A0.156%2B%205%2A0.031%20%3D%202.5)
We can find the second moment given by:
![E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 0^2*0.031 +1^2*0.156+ 2^2*0.313+3^2*0.313+ 4^2*0.156+ 5^2*0.031 =7.496](https://tex.z-dn.net/?f=%20E%28X%5E2%29%20%3D%20%5Csum_%7Bi%3D1%7D%5En%20X%5E2_i%20P%28X_i%29%20%3D%200%5E2%2A0.031%20%2B1%5E2%2A0.156%2B%202%5E2%2A0.313%2B3%5E2%2A0.313%2B%204%5E2%2A0.156%2B%205%5E2%2A0.031%20%3D7.496%20)
And we can calculate the variance with this formula:
![Var(X) =E(X^2) -[E(X)]^2 = 7.496 -(2.5)^2 = 1.246](https://tex.z-dn.net/?f=%20Var%28X%29%20%3DE%28X%5E2%29%20-%5BE%28X%29%5D%5E2%20%3D%207.496%20-%282.5%29%5E2%20%3D%201.246)
And the deviation is:
![Sd(X) = \sqrt{1.246}= 1.116](https://tex.z-dn.net/?f=%20Sd%28X%29%20%3D%20%5Csqrt%7B1.246%7D%3D%201.116)
Step-by-step explanation:
For this case we have the following probability distribution given:
X 0 1 2 3 4 5
P(X) 0.031 0.156 0.313 0.313 0.156 0.031
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).
We can verify that:
![\sum_{i=1}^n P(X_i) = 1](https://tex.z-dn.net/?f=%20%5Csum_%7Bi%3D1%7D%5En%20P%28X_i%29%20%3D%201)
And ![P(X_i) \geq 0, \forall x_i](https://tex.z-dn.net/?f=%20P%28X_i%29%20%5Cgeq%200%2C%20%5Cforall%20x_i)
So then we have a probability distribution
We can calculate the expected value with the following formula:
![E(X) = \sum_{i=1}^n X_i P(X_i) = 0*0.031 +1*0.156+ 2*0.313+3*0.313+ 4*0.156+ 5*0.031 = 2.5](https://tex.z-dn.net/?f=%20E%28X%29%20%3D%20%5Csum_%7Bi%3D1%7D%5En%20X_i%20P%28X_i%29%20%3D%200%2A0.031%20%2B1%2A0.156%2B%202%2A0.313%2B3%2A0.313%2B%204%2A0.156%2B%205%2A0.031%20%3D%202.5)
We can find the second moment given by:
![E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 0^2*0.031 +1^2*0.156+ 2^2*0.313+3^2*0.313+ 4^2*0.156+ 5^2*0.031 =7.496](https://tex.z-dn.net/?f=%20E%28X%5E2%29%20%3D%20%5Csum_%7Bi%3D1%7D%5En%20X%5E2_i%20P%28X_i%29%20%3D%200%5E2%2A0.031%20%2B1%5E2%2A0.156%2B%202%5E2%2A0.313%2B3%5E2%2A0.313%2B%204%5E2%2A0.156%2B%205%5E2%2A0.031%20%3D7.496%20)
And we can calculate the variance with this formula:
![Var(X) =E(X^2) -[E(X)]^2 = 7.496 -(2.5)^2 = 1.246](https://tex.z-dn.net/?f=%20Var%28X%29%20%3DE%28X%5E2%29%20-%5BE%28X%29%5D%5E2%20%3D%207.496%20-%282.5%29%5E2%20%3D%201.246)
And the deviation is:
![Sd(X) = \sqrt{1.246}= 1.116](https://tex.z-dn.net/?f=%20Sd%28X%29%20%3D%20%5Csqrt%7B1.246%7D%3D%201.116)
Answer:
54.6
Step-by-step explanation:
42 = 70%
100% - 70% = .30%
42 x 1.3 = 54.6