Question 1162665: I need to create an excel worksheet for this problem.
High School Dropouts: Approximately 10.3% of American high school students drop out of school before graduation. Choose 10 students entering high school at random. Find the probability that:
No more than two drop out
At least 6 graduates
All 10 stay in school and graduate
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! p = .103
this is the probability that a randomly selected student will drop out.
q = 1 - .103 = .897
this is the probability that a randomly selected student will not drop out, i.e. the student will graduate.
this is a binomial probability type problem as far as i can tell.
the basic equation is:
p(x) = c(n,x) * p^x * q^(n-x).
when n = 10, the equation becomes:
p(x) = c(10,x) * p^x * q^(n-x)
this equation is applied for x = 0 to 10.
the following excel spreadsheet printout shows you the complete probability workup plus the results of the analysis for the questions asked.
the questions and their answers are shown below:
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1) No more than two drop out.
this would be the sum of p(0) + p(1) + p(2).
that's the sum of cells I4, I5, I6.
that's equal to .924549334 which is the result shown in cell I16.
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2) At least 6 graduate.
this is equivalent to not more than 4 drop out.
that's the sum of cells I4, I5, I6, I7, I8.
that's equal to .998130062 which is the result shown in cell I17.
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3) All 10 stay in school and graduate.
this is equivalent to 0 drop out.
that's the results shown in cell I4.
that's equal to .337228624 which is the result shown in cell I4 and I18.
____________________________________________
cell numbering is column letter followed by row number.
consequently, the value in cell I18 means the value that's in the cell whose position is at column I row 18 of the spreadsheet.
some examples:
value in cell G4 is 1
value in cell C14 is 10
value in cell H8 is .520900361
c(n,x) is the number of ways you can get x elements out of a set of n elements when ordering of the elements is not considered.
the formula is c(n,x) = n! / (x! * (n-x)!)
for example, when n = 10 and x = 4, the formula becomes c(10,4) = 10! / (4! * 6!).
this is equal to 10*9*8*7*6*5*4*2*1 / (4*3*2*1 * 6*5*4*3*2*1)
6*5*4*3*2*1 in the numerator and the denominator cancel out and you are left with 10*9*8*7/(4*3*2*1) which is equal to 210.
that's the value that's in cel F8 in the spreadsheet.
fortunately, excel has a formula to do that for you.
for example, the formula in cell F8 is =combin(10,C8).
excel takes the value in cell C8 and uses it to find the result of the combination formula for n = 10 and x = 4.
the display in cell F8 is the result of the operation which is 210.
columns J, K, and L are just showing you which cells in column I are summed up to give you the results in cells I16, I17, I38.
column J shows you that cells I4,I5,I6 are summed up to give you the results in cell I16.
column K shows you that cells I4,I5,I6,I7,I8 are summed up to give you the results in cell I17.
column L shows you that the cell I4 is the cell that is used to give you the results in cell I18.
note that the results shown in column I are the produce ot the results in columns F, G, H.
for example, the value in cell I6 is equal to the value in cell F6 * G6 * H6.
this becomes .200090518 = 45 * .010609 * .419122228.
if you do the calculations, you might be off by a very small amount.
this is because the numbers displayed in the cells are rounded to the number of digits that are displayed in those cells if the number of actual digits in those numbers is greater than the number of digits displayed.
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