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]
