Respuesta :
Answer: 0.7264
Explanation:
The number of independent questions (n) = 100
Probability of answering a question (p) = 0.80
Let X be the no. of questions that need to be answered.
[tex]\therefore[/tex] random variable X follows binomial distribution
The probability function of a binomial distribution is given as
[tex]P(X=x) = \binom{n}{x}\times p^{x}(1-p)^{n-x}[/tex]
Now , we nee to find P(74 ≤ X ≤ 84)
[tex]\therefore P(74\leq X\leq 84) = P(X=74) + P(X=75).........+ P(X=84)[/tex]
P(74 ≤ X ≤ 84) = [tex]\sum_{74}^{84}\binom{100}{x}\times (0.80)^{x}(0.20)^{100-x}[/tex]
P(74 ≤ X ≤ 84) = 0.7264
