Suppose a college is considering a new placement test, which

Humberto Winters

Humberto Winters

Answered question

2022-02-12

Suppose a college is considering a new placement test, which has 40% of all students taking remedial arithmetic. If 8 randomly chosen students take the placement test, what is the probability that exactly 2 of them will have to take remedial arithmetic?

Answer & Explanation

merquilhi8fd

merquilhi8fd

Beginner2022-02-13Added 11 answers

Each student has an independent chance of 0.4 (or 40%) of taking remedial arithmetic. Assuming the population of students is large enough that sampling without replacement does not affect that 40% probability for the remaining students, we can apply the Binomial theorem.
Let X be the number of students chosen out of 8 that will have to take remedial arithmetic. Then X is B(n=8,p=0.4). So
P(X=x)=(nx)px(1p)nx=(8x)0.4x(0.6)8x
and so P(X=2)=(82)0.42(0.6)6
=28(0.16)(0.046656)
=0.20901888
0.209
=20.9%

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