A distribution of grades in a course where A=4, B=3, etc.

X=0, 1, 2, 3, 4

P(X)=0.1, 0.17, 0.21, 0.32, 0.2

a. Find the probability that a student has passed this class with at least a C (at least a 2)

b. Find the probability that a student has an A (4) given that he has passed the class with at least a C (2).

c. Find the expected grade in this class

d. Find the variance and standard deviation for the class grades.

e. Suppose a student knows they passed the course with a C, what should they expect their grade to be?

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

                         4       0.2               0.8           16       3.2  

∑                     10          1                   2.35         30     7.09

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

10/60

step-by-step explanation:

if you divide 10 by 60 the answer is 0.166666 while if you divide or solve the other problems it equals 0.6

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet