Question

Studies have documented that 75% of college business students cheat on final exams. A business professor monitored a random sample of 40 students via web cameras as they took their final exam.The probability that exactly 30 of the students monitored cheat on the final exam is:(Round your answer to 4 decimal places)

Answer 1

The probability is 0.1444.

Explanation:

Let X be the event that college business students cheated on final exams,

Since, the probability that student cheats on exam, p = 75 % = 0.75,

So, the probability that student does not cheat on exam, q = 1 - p = 0.25,

The binomial distribution formula,

`P(x)=^nC_r p^r q^(n-r)`

Where,
`^nC_r=(n!)/(r!(n-r)!)`

The probability that exactly 30 of the students monitored cheat on the final exam out of 40 students is,

`P(X=30)=^(40)C_(30) 0.75^(30) 0.25^(40-30)`

`=847660528* 0.75^(30) * 0.25^(10)`

`=0.144364346356`

`\approx 0.1444`