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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)

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4 votes

Answer:

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

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