In a local college, 20\% of the math majors are

Vagotonusybk

Vagotonusybk

Answered question

2022-02-11

In a local college, 20% of the math majors are women. Ten math majors are chosen at random.
a. What is the probability that exactly 2 are women?
b. How do you find the mean and the variance?

Answer & Explanation

Clark Carson

Clark Carson

Beginner2022-02-12Added 17 answers

Step 1
P(X=2), n=10, p=0.2
XBinomial(n=10, p=0.2)
P(X=2)=(nx)px(1p)nx=(102)(0.2)2(10.2)102
=45×(0.2)2(0.8)8
=0.301990.3019900.302
P(X=2)=0.302
Step 2
P(X2), n=10, p=0.2
(X2)=P(0X2)=P(X=0, 1, 2)
=P(X=0)+P(X=1)+P(X=2) (because these are disjoint events)
P(X=0)=(100)(0.2)0(10.2)10=1(0.2)0(0.8)100.107374
P(X=1)=(101)(0.2)1(10.2)9=10(0.2)1(0.8)9=≈0.268435
P(X=2)=(102)(0.2)2(10.2)8=45(0.2)2(0.8)80.30199
P(X=0)+P(X=1)+P(X=2)
=0.107374+0.268435+0.30199=0.6777990.678
P(X2)=0.678
Step 3
P(X=0), n=10, p=0.2
XBinomial(n=10, p=0.2)

Johnathan Carpenter

Johnathan Carpenter

Beginner2022-02-13Added 12 answers

Step 1
b) Mean,
μ=n×p=10×0.2=2
Variance,
s=n×p×(1p)=10×0.2×(10.2)=1.6

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