Question

R.H Bruskin Associates Market Research found that 40% of Americans do not think having a college education is important to succeed in the business world. If a random sample of 5 americans is selected, find these probabilities:
a. Exactly two people will agree w/ that statement
b. At most 3 people will agree w/ that statement
c. At least 2 people will agree
d. Fewer than 3 people will agree

Answer 1

a. 5C2(2/5)^2(3/5)^3 = 216/625 or 0.346
is this correct?

Answer 2

Yeah,. you are right. Sorry I made a mistake earlier
@daniell102

Answer 3

@ash2326 what about b,c, and d. do you know how to solve them?

Answer 4

may i know the answer of b?
do you know??

Answer 5

no, i'm still trying to figure it out

Answer 6

We seek the probability of at most 3 successes, i.e., selecting 0, 1, 2, or 3 (but no more than) people who agree with
the given statement. So, X _< 3 and P(X _< 3) = P(X = 0)+P(X = 1)+P(X = 2)+P(X = 3). You can attack this a couple
of different ways. You can find each of these probabilities and add them all up, or you can find the probability of
the complement and subtract that from 1. The complement of X _<3 is X >_ 4 and
P(X >_ 4) = P(X = 4)+P(X = 5).
I’ll do it both ways (remember we have P(X=2) above):
P(X=0) = 5 C 0 (0.4)0(0.6)5 = 5!/0!5!(1)*(0.07776) = 0.07776

P(X=1) = 5 C 1 (0.4)1(0.6)4 = 5/1!4!(0.4)*(0.1296) = 5*0.05184 = 0.2592

P(X=3) = 5 C 3 (0.4)3(0.6)2 = 5!/2!3!(0.064)*(0.36) = 10*0.02304 = 0.2304
Add all these and we get P(X _< 3) = 0.07776 + 0.2592 +0.3456 + 0.2304 = 0.91296.
P(X=4) = 5 C 4 (0.4)4(0.6)1 = 5!/1!4!(0.0256)*(0.6) = 5*0.01536 = 0.0768

P(X=5) = 5 C 5 (0.4)5(0.6)0 = 5!/5!0!(0.01024) = 0.01024


Add these and subtract from 1: P(X _< 3) = 1- (0.0768 + 0.01024) = 1- 0.08704 = 0.91296.
c. At least 2 people will agree with that statement.
Since we have all the numbers listed in the first two parts of the problem, we just need to sort out the English
and add the correct ones. At least 2 people means 2 or more people, so the probability we seek is
P(X _> 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
= 0.3456 + 0.2304 + 0.0768 + 0.01024
= 0.66304.
Alternatively, we could use the complement and we get
P(X _> 2) = 1 - P(X _< 1) = 1 - (P(X = 0)+P(X = 1))
= 1 - (0.07776 +0.2592)
= 0.66304.
d. Fewer than 3 people will agree with that statement.
Fewer than 3 people means strictly less than 3 (it can not be 3), so we’re looking for
P(X _< 2) = P(X = 0)+P(X = 1)+P(X = 2)
= 0.07776 + 0.2592 +0.3456
= 0.68256.