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: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,[tex]P(x)=^nC_r p^r q^{n-r}[/tex]Where, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex] The probability that exactly 30 of the students monitored cheat on the final exam out of 40 students is,[tex]P(X=30)=^{40}C_{30} 0.75^{30} 0.25^{40-30}[/tex][tex]=847660528\times 0.75^{30} \times 0.25^{10}[/tex][tex]=0.144364346356[/tex][tex]\approx 0.1444[/tex]