Answer:
a. P(x= at least 2)= 1- P(no pass)= 1- 0.27= 0.73
b. 0.55
c. Expected Value = mean = 2.35 which is more than C grade that is grade B
d. variance= 1.5675
standard deviation =1.252
e. Their grade would be from (73- 100)
or 3 as it has the highest probability
Step-by-step explanation:
X P(X) X .P(X) X² X².P(X)
0 0.1 0 0 0
1 0.17 0.17 1 0.17
2 0.21 0.42 4 0.84
3 0.32 0.96 9 2.88
<u> 4 0.2 0.8 16 3.2 </u>
<u>∑ 10 1 2.35 30 7.09</u>
Let X represent an event that the student has passed with at least a 2.
The probability of not passing (or below 2) is 0.1+ 0.17= 0.27
Then using law of complementation
a. P(x= at least 2)= 1- P(no pass)= 1- 0.27= 0.73
b. Let Y represent the event that a student has an A (4) given that he has passed the class with at least a C (2)
P(x)= 0.73
P(A)= 0.4
P(Y)= P(A)/P(X)= 0.4/0.73=0.55
c. Expected value= mean = 2.35 which is greater than C , Hence grade B
First we find the mean ∑X.P(X)= 2.35
d. Variance = ∑X².P(X) - (∑X.P(X)²= 7.09- (2.35)² = 7.09- 5.5225=1.5675
Standard Deviation = square root of Variance = √1.5675= 1.252
e. P(all pass) = P(A) +P(B) +P(C)= 0.2+ 0.32+ 0.21= 0.73
