Respuesta :
Answer:
0.7667 = 76.67% probability that at least 2 graduates have a summer job
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Forty percent of all high school graduate work during the summer to earn money for college tuition for the upcoming fall term.
This means that [tex]p = 0.4[/tex]
6 graduates.
This means that [tex]n = 6[/tex]
What is the probability that at least 2 graduates have a summer job
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.4)^{0}.(0.6)^{6} = 0.0467[/tex]
[tex]P(X = 1) = C_{6,1}.(0.4)^{1}.(0.6)^{5} = 0.1866[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0467 + 0.1866 = 0.2333[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.2333 = 0.7667[/tex]
0.7667 = 76.67% probability that at least 2 graduates have a summer job
