Answer:The following data gives the scores of 13 students in a Biostatistics exam. 75 80 28 70 95 82 75 64 61 90 81 65 91 a) Find the following statistical measures 1. Mean 2. Median 3. Mode 4. Range 5. 34th percentile 6. Interquartile Range 7. Variance 8. Standard deviation PRINCIPLES OF STATISTICS Assignment (1) Due Date: 15/7/2020 9. Coefficient of variation. b) (Without Calculations) If the instructor decide to add up 5 marks for every student, what are the values of the statistical measures mentioned in part (a). c) Construct the Boxplot of students' scores, and identify any possible outliers.
Answer:
![P( A \cap B) = P(A) *P(B) = 0.34*0.32 = 0.1088](https://tex.z-dn.net/?f=%20P%28%20A%20%5Ccap%20B%29%20%3D%20P%28A%29%20%2AP%28B%29%20%3D%200.34%2A0.32%20%3D%200.1088)
And then replacing in the total probability formula we got:
![P(A \cup B) = 0.34+0.32 - 0.1088 = 0.5512](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%29%20%3D%200.34%2B0.32%20-%200.1088%20%3D%200.5512)
And rounded we got ![P(A \cup B ) = 0.551](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%20%29%20%3D%200.551)
That represent the probability that it rains over the weekend (either Saturday or Sunday)
Step-by-step explanation:
We can define the following notaton for the events:
A = It rains over the Saturday
B = It rains over the Sunday
We have the probabilities for these two events given:
![P(A) = 0.34 , P(B) = 0.32](https://tex.z-dn.net/?f=%20P%28A%29%20%3D%200.34%20%2C%20P%28B%29%20%3D%200.32)
And we are interested on the probability that it rains over the weekend (either Saturday or Sunday), so we want to find this probability:
![P(A \cup B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%29)
And for this case we can use the total probability rule given by:
![P(A \cup B) = P(A) + P(B) - P(A \cap B)](https://tex.z-dn.net/?f=P%28A%20%5Ccup%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29%20-%20P%28A%20%5Ccap%20B%29)
And since we are assuming the events independent we can find the probability of intersection like this:
![P( A \cap B) = P(A) *P(B) = 0.34*0.32 = 0.1088](https://tex.z-dn.net/?f=%20P%28%20A%20%5Ccap%20B%29%20%3D%20P%28A%29%20%2AP%28B%29%20%3D%200.34%2A0.32%20%3D%200.1088)
And then replacing in the total probability formula we got:
![P(A \cup B) = 0.34+0.32 - 0.1088 = 0.5512](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%29%20%3D%200.34%2B0.32%20-%200.1088%20%3D%200.5512)
And rounded we got ![P(A \cup B ) = 0.551](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%20%29%20%3D%200.551)
That represent the probability that it rains over the weekend (either Saturday or Sunday)
Slope-intercept form is y = mx + b.
In this form, m is slope and b is y-intercept.
Slope is rise over run. The formula for this is (y2-y1)/(x2-x1).
Y-intercept is the value of y when x is equal to 0.
1. Slope = 8 ; Y-intercept = 0
y = mx + b
m = 8 ; b = 0
y = 8x + 0
y = 8x
2. Slope = 1 ; Y-intercept = 2
y = mx + b
m = 1 ; b = 2
y = 1x + 2
y = x + 2
The answer to #1 is y = 8x.
The answer to #2 is y = x + 2.
Hope this helps!