Answer:
(a) 100
(b) 10.27
Step-by-step explanation:
We are given
No of elements = 15
Σ(x-c) = 72,Σ(x-c)^2 = 499.6
,where c is a constant
and the sample mean is 104.8.
(a) lets take into account Σ(x-c) = 72
this means that we have the sum of the 15 elements of x and each element of x is subtracted by the constant c
so the equation becomes Σxi -15c = 72, ............(1)
where xi means the sum of the elements of x from 1 to 15.
we are given the mean as 104.8
this means that Σxi/15 = 104.8
Σxi = 15*104.8 = 1572 .............(2)
substituting (2) in (1)
we get
1572 - 15c = 72
15c = 1500
c = 100
(b) We will use the property that variance does not change when a constant value is added or subtracted to the elements. This we can observe in the given equation that c is a constant that has the value of 100.
so the variance is
σ^2 = Σ(x-c)^2/15 - (Σ(x-c)/15 )^2
= 499.6/15 - (72/15)^2
= 33.31 - 23.04
σ^2 = 10.27
Therefore the variance of the given problem is 10.27.
GPA = 3.59
For calculating the GPA, first calculate the quality points for each grade and course and then add them up like shown below:
A - 4 points x 33 credit hours = 132 quality points
B - ( 3 points x 2 credit hours ) x 3 (because there are 3 courses) = 18 quality points
C - 2 points x 3 credits = 6 quality points
D - 1 point x 2 credits = 2 quality points
Now add up all the quality points = 132 + 18 + 6 + 2 = 158
Add the credit hours as well = 33 + 6 + 3 + 2 = 44
Divide the total quality points by total credit hours to get the GPA = 158/44 = 3.59
i hope it helps please mark me as brainliest please
The answer is 8/25
Hope it helped
