Question

A recent survey found that 70% of Indiana rivers State College students plan to go on a vacation after graduation suppose 5% of Indiana rivers State College students are randomly selected and let X be the number of students that plans to go on a vacation after graduation out of the sample of 5 used a binomial probability formula or the binomial probability table to construct the probability distribution of X also used a binomial probability formula or the binomial probability table to construct the cumulative probability distribution

Answer 1

Given:

Probability of Indiana rivers State College students plan to go on a vacation after graduation is(P) 70%=0.7.

Sample size =n=5

x= the random sample of number of students that plans to go on a vacation after graduation out of the sample of 5

The formula for binomial distribution is,

`\begin{gathered} P(X=x)=^nC_x(p)^x(q)^(n-x) \\ \text{Here, p=0.7} \\ q=1-p=1-0.7=0.3 \\ ^nC_x=(n!)/(x!(n-x)!) \end{gathered}`

The probability that no more than 4 students out of random sample of 5 students plan to go on vaccination after graduation is given by,

Hence, the probability P(X≤4)=0.832.