Question

Assume that on a standardized test of 100 questions, a person has a probability of 80% of answering any particular question correctly. Find the probability of answering between 74 and 84 questions

Answer 1

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.

$\therefore$ random variable X follows binomial distribution

The probability function of a binomial distribution is given as

$P(X=x) = \binom{n}{x}\times p^{x}(1-p)^{n-x}$

Now , we nee to find P(74 ≤ X ≤ 84)

$\therefore P(74\leq X\leq 84) = P(X=74) + P(X=75).........+ P(X=84)$

P(74 ≤ X ≤ 84) = $\sum_{74}^{84}\binom{100}{x}\times (0.80)^{x}(0.20)^{100-x}$

P(74 ≤ X ≤ 84) = 0.7264