Statistics Question: a) Approximately 84% of the students in this class make les

Question

Statistics Question:

a) Approximately 84% of the students in this class make less than $20,000 a year. If 7 students are randomly selected, find the probability that more than 3 students make less than $20,000 a year.

b) Approximately 16% of the students in this class make between $20,000 and $49, 999 a year. If 7 students are randomly selected, find the probability that at most 3 students make between $20,000 and $49,999 a year.

c) Approximately 16% of the students in this class make between $20,000 and $49, 999 a year. If 9 students are randomly selected, find the probability that exactly 2 students make between $20,000 and $49,999 a year.

Explanation / Answer

The binomial distribution describes the behaviour of a count variable X if the following conditions apply:

1: The number of observations n is fixed.

2: Each observation is independent.

3: Each observation represents one of two outcomes ("success" or "failure").

4: The probability of "success" p is the same for each outcome.

Here for all the 3 questions, n is fixed, each observation is independent as result of one student will not affect result of another student, only two outcomes and probability of success is same.Hence we will use binomial distribution to get answer for requred probability.

a. Here p=0.84, n=7 and x=3

P(x>3)=Sum(ncxp^x(1-p)^n-x), x=3,4,5....7

P(x>3)=0.9847

b. Here p=0.16, n=7 and x=3

So P(x<=3)=Sum(ncxp^x(1-p)^n-x), x=1,2,3

P(x<=3)=0.9847

c. Here p=0.16, n=9 and x=2

P(x=2)=9c2*0.16^2*(1-0.16)^7=0.2720

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