Question

In a certain college, 36% of the physics majors belong to ethnic minorities. If 12 studentsare selected at random from the physics majors, what is the probability that no morethan 5 belong to an ethnic minority?0 78.94%23.52%76.48%O 21.06%

Answer 1

The variable of interest is:

X: number of students of the Physics majors that belong to ethnic minorities in a sample of 12

The probability of success is p=0.36

You have to calculate the probability of at most 5 of the 12 students belong to an ethnic minotiry, symbolically:

P(X≤5)

You have to use a table of binomial distribution to answer this. Input the sample size, the number of successes and the probability of success and you'll get that the probability is:

P(X≤5)=0.76476

Multiply the probability by 100 to express it as a percentage:

0.76476*100=76.476%=76.48%

Correct answer is the third one.