There are 33 students in JJHSs 9th grade Algebra class. 14 of these students are

Question

There are 33 students in JJHSs 9th grade Algebra class. 14 of these students are female and 19 are male. 8 students from the class are randomly selected for automatic As. Let X = the number of selected students who are female.  

a. What is the probability that none of the selected students are female?
b. What is the probability 5 or fewer of the selected students are female?
c. What is the probability that more than 5 of the selected students are female?
d. What is the expected value of X?
e. What is the standard deviation of X?
f. What is the probability that X is within 1 standard deviation of its expected value?
g. If we select the students in the class one by one until we select a female then what is the probability that we have to select more than 3 students?

Explanation / Answer

a)

14C0*19C8/33C8= 1*75582/13884156=0.005444

b)

14C5*19C3/33C8+14C4*19C4/33C8+14C3*19C5/33C8+14C2*19C6/33C8+14C1*19C7/33C8+14C0*19C8/33C8=

2002*969/13884156+1001*3876/13884156+364*11628/13884156+91*27132/13884156*14*50388/13884156+1*75582/13884156=0.958102

c)

1-0.958102=0.041898

d)

Expected value would be 1

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