Answer to Question #123097 in Statistics and Probability for Joms

Question

The Department of Labor and Employment (DOLE) found that 83% of the Filipinos think that having a college education is important to succeed in life. If a ramdom sample of seven(7) Filipinos is selected, find the probability that the exactly four (4) people will agree with that statement (use Binomial Distribution

Answer 1

Let, X = the random variable denoting the number of people will agree with the given statement, X = 0, 1, ... , 7.

We have 83% of the Filipinos think that having a college education is important to succeed in life i.e. the probability of people agreeing with this statement is 83% = 0.83.

Then X ~ bin(n = 7, p = 0.83)

The p.m.f. of X is given by,

P(X = x) $= \begin{cases} \dbinom{7}{x}(0.83)^x(1-0.83)^{7-x} &\text{for } x=0,1,...,7 \\ 0 &\text{otherwise } \end{cases}$

Now, the probability that the exactly 4 people will agree with that statement

= P(X = 4)

= $\dbinom{7}{4}(0.83)^4(1-0.83)^{7-4}$

= 0.0816 (rounded to 4 decimal places)

Answer: The probability that exactly four people will agree with the given statement is 0.0816.