Answer :
The probability that out of 20 randomly chosen students entering college, less than 3 drop out = 0.11674
Let X be a random variable representing the number of students drop out from college such that X follows binomial distribution.
A binomial distribution deals with two possibilities in 'n' trials - success or failure. Here the case of success is being drop out from college.
The probability distribution function of a binomial distribution is,
P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ , where n is the number of trials,
p - the probability of success
Here, n = 20 since 20 students are selected randomly.
Since 20% of the students entering college drop out before receiving their diplomas, probability of being drop out = 20/100 = 0.2
Probability that less than 3 students = P(X<3)
= P( X = 0 or 1 or 2)
= P(X= 0) + P(X= 1) + P(X= 2)
Now, P(X=0) = ²⁰C₀ (0.2)⁰ (1-0.2)²⁰⁻⁰
= 1 x 1 x 0.01153
= 0.01153
P(X = 1) = ²⁰C₁ (0.2)¹ (1-0.2)²⁰⁻¹
= 20 x 0.2 x 0.8¹⁹
= 0.05765
P(X = 2) = ²⁰C₂ (0.2)² (1-0.2)²⁰⁻²
= 66 x (0. 2)² x 0.8¹⁸
= 0.04756
Therefore, The probability that out of 20 randomly chosen students entering college, less than 3 drop out = P(X= 0) + P(X= 1) + P(X= 2)
= 0.01153 + 0.05765 + 0.04756
= 0.11674
Learn more about binomial distributions at https://brainly.com/question/15246027
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