Respuesta :
The binomial distribution is applicable when only two outcomes are possible. The probability that the newspaper staff receives quotes from exactly 3 athletes is 0.1238.
What is Binomial distribution?
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given that 18 of the senior DLT members are athletes, therefore, the probability of a DLT member being an athlete is,
[tex]P = \dfrac{18}{30} = \dfrac{6}{10} = 0.6[/tex]
Also, 12 of the senior DLT members are non-athletes, therefore, therefore, the probability of a DLT member being a non-athlete is,
[tex]q = \dfrac{12}{30} = \dfrac{4}{10} = 0.4[/tex]
Now, using the binomial distribution the probability that the newspaper staff receives quotes from exactly 3 athletes can be written as,
[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=3) = ^8C_3\cdot (0.6)^3\cdot (0.4)^{(8-3)}\\\\P(x=3) = ^8C_3\cdot (0.6)^3\cdot (0.4)^{(5)}\\\\P(x=3) = 0.1238[/tex]
Hence, the probability that the newspaper staff receives quotes from exactly 3 athletes is 0.1238.
Learn more about Binomial Distribution:
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