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

Answer:

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

Step-by-step 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........

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