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

Answer:

The probability is 0.1444.

Step-by-step 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, $^nC_r=\frac{n!}{r!(n-r)!}$

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

$P(X=30)=^{40}C_{30} 0.75^{30} 0.25^{40-30}$

$=847660528\times 0.75^{30} \times 0.25^{10}$

$=0.144364346356$

$\approx 0.1444$