Question

Indian River State College has stated in the 2019 through 2020 academic year 39 posts of a student or 1st generation college student suppose you take a random sample of 5RSC student and ask if they are 1st generation college students or not counting the numbers of the 1st generation student use this experience to answer the falling question around solutions for decimal places

Answer 1

In this question, we are asked to create a binomial probability distribution table.

The binomial probability applies when an event can either result in success or not, which is the case for being (success) or not a first-generation student.

If the probability of success is p, then the binomial probability distribution P(x) of having x successes out of n events is given by the formula:

`P(x)=C(x,n)\cdot p^x\cdot(1-p)^(n-x)`

where C(x,n) represents the number of combinations of x elements out of n.

Part A:

In this case, we have:

p = 39% = 0.39

n = 5

Then, the probabilities are:

`\begin{gathered} P(0)=C(0,5)\cdot0.39^0\cdot(1-0.39)^(5-0)=1\cdot1\cdot0.61^5\cong0.0845 \\ \\ P(1)=C(1,5)\cdot0.39^1\cdot(1-0.39)^(5-1)=5\cdot0.39\cdot0.61^4\cong0.2700 \\ \\ P(2)=C(2,5)\cdot0.39^2\cdot(1-0.39)^(5-2)=10\cdot0.39^2\cdot0.61^3\cong0.3452 \\ \\ P(3)=C(3,5)\cdot0.39^3\cdot(1-0.39)^(5-3)=10\cdot0.39^3\cdot0.61^2\cong0.2207 \\ \\ P(4)=C(4,5)\cdot0.39^4\cdot(1-0.39)^(5-4)=5\cdot0.39^4\cdot0.61^1\cong0.0706 \\ \\ P(5)=C(5,5)\cdot0.39^5\cdot(1-0.39)^0=1\cdot0.39^5\cdot1\cong0.0090 \end{gathered}`