You are trying to solve for n, the number of residents you would expect to be randomly selected,
given that 21% had earned at least a bachelor’s degree. The probability of a “success” is 21% or
0.21.
10 = n(0.21)
Divide by 0.21
n = 47.619…. always round UP even if the decimal is not above 0.5 (because you can never have
“part” of a person  )
So n = 48.
b) This a little atypical because in order to use the calculator (which you definitely want to do – it would
take FOREVER by hand), you have to use ‘trial and error’ to get the probability you are looking for. You
are actually looking for n, the total number of people you’d need for there to be a probability of 0.851
for there to be at least 10 people to have earned a Bachelor’s degree. This means that if there are more
than 10 people, you’d have to add up the probability of 10, 11, 12, 13, 14, 15, … all the way up to
whatever “n” is.
So instead we find the complement of this, 1 – P(0 through 9) In other words, if we take 100% or 1, and
subtract the probability of there being 1 through 9 people with Bach. degrees, we will find the
probability we are looking for.
So, we want 1 – P(0 through 9) to be equal to 0.851.
If 1 - P(0 through 9) = 0.851 then we need P(0 through 9) to be 0.149. (because 1 – 0.149 = 0.851)
So basically we are going to try various numbers for n until we get binomcdf(n, p, x) to be 0.149
From the problem we know that p = 0.21 and we are using x = 9 because binomcdf will find the SUM of
probabilities of 0 through 9 people having at least a Bach. degree.
So we will try binomcdf(n, 0.21, 9) until we find the “right” n value.
Honestly, take your best guess and see how close you get. ;)
I started out with n = 30 ( I just picked a number larger than 9 to see what I’d get)
not even close!
getting better! (the higher “n” is, the probability is getting smaller which
makes sense)
too small!!
So we know it’s between 50 and 70.
very close! We are trying to get to 0.149
too small - so we need a lower n value
This is as close as we are going to get since we can’t have a decimal for the
n value. Since n = 60 was too high and n = 62 was too low and n = 61 while not “exact” is the closest we
found, we must choose that as our answer.
So, the answer is n = 61.
And now we all need this . . .