There are 33 students in JJHSs 9th grade Algebra class. 14 of these students are
ID: 2925853 • Letter: T
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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