Question
Asked Nov 9, 2019
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77% of all students at a college still need to take another math class. If 5 students are randomly selected, find the probability that

a. Exactly 2 of them need to take another math class. 
b. At most 2 of them need to take another math class. 
c. At least 3 of them need to take another math class.

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Expert Answer

Step 1

Binomial distribution:

The binomial distribution gives the probability of number of successes out of n trials in a series of Bernoulli trials.

The probability mass function (pmf) of a binomial random variable X is given as:

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хп-х Р(х -к)-()Р |P'а, х3D0,1,..., n;0 <p<1;q %3D1-р otherwise

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Step 2

a.Computing the probability that exactly 2 of them need to take another math class:

It is given that 77% of the students need to take another math class.

A sample of 5 students is selected.

Thus, n = 5 and p = 0.77.

Define the random variable X as the number of students needs to take another math class.

The probability that exactly 2 of them need to take another math class is obtained as follows:

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|Using the EXCEL formula, P(X 2) 0.0721 BINOM.DIST(2,5,0.77,0)

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Step 3

b.Computing the probability that at most 2 of them need to take another math class:

The probability t...

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Using the EXCEL formula, =BINOM.DIST (2,5,0.77,1) P(X 2) 0.0836|

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