Answer: 4.54%
Step-by-step explanation:
The binomial probability formula :-
[tex]P(X)=^nC_x \ p^x\ (1-p)^{n-x}[/tex], where P(x) is the probability of getting success in x trials, n is total number of trials and p is the probability of getting succes in each trial.
Given : The proportion of college freshmen majoring in business said that "to get training for a specific career" was a very important reason for their going to college : [tex]p=0.736[/tex]
Now, if six freshman business majors selected at random, then the probability that no more than two of the six freshmen in the group felt that this reason was very important. :-
[tex]P(x\leq2)=P(0)+P(1)+P(2)\\\\=^6C_0 \ (0.736)^0\ (1-0.736)^{6}+^6C_1 \ (0.736)^1\ (1-0.736)^{5}+^6C_2 \ (0.736)^2\ (1-0.736)^{4}\\\\=(0.264)^6+6(0.736)(0.264)^5+15(0.736)^2(0.264)^4\\\\=0.04547116664\approx0.0454=4.54\%[/tex]
Hence, the probability that no more than two of the six freshmen in the group felt that this reason was very important= 4.54 %
