Question

26% of college students live in campus housing. a random sample of 15 college students is selected. find the probability that 10 or more students will live in campus housing

Answer 1

The probability that 10 or more students will live in campus housing is approximately 0.111%

Explanation:

Binomial distribution formula:

If the probability of success is
`p`, then the probability of
`r` successes out of
`n` trials will be:
`^nC_(r)(p)^r(1-p)^n^-^r`

26% of college students live in campus housing. So here,
`p= 26\%= 0.26`

A random sample of 15 college students is selected. So,
`n= 15`

Now, "10 or more students" means 10 or 11 or 12 or 13 or 14 or 15 students. That means,
`r= 10, 11, 12, 13, 14, 15`

Thus, the probability that 10 or more students will live in campus housing will be........

`[^1^5C_(10)(0.26)^1^0(1-0.26)^5]+[^1^5C_(11)(0.26)^1^1(1-0.26)^4]+[^1^5C_(12)(0.26)^1^2(1-0.26)^3]+[^1^5C_(13)(0.26)^1^3(1-0.26)^2]+[^1^5C_(14)(0.26)^1^4(1-0.26)^1]+[^1^5C_(15)(0.26)^1^5(1-0.26)^0]\\ \\ = 0.00094...+0.00015...+0.00001...+ 0.0000014...+ 0.000000071...+0.0000000016...\\ \\ =0.00111002... =0.111002...\% \approx 0.111\%`