Question

A study conducted at a certain college shows that​ 65% of the​ school's graduates find a job in their chosen field within a year after graduation. Find the probability that 11 randomly selected graduates all find jobs in their chosen field within a year of graduating. Round to the nearest thousandth if necessary. Round to three decimal places as needed.

Answer 1

Answer: 0.009

Step-by-step explanation:

Formula we use here : Binomial distribution formula

Probability of getting success sin x trial =$P(X)=^nC_xp^x(1-p)^{n-x}$ , where n is the sample size and p is the probability of success in each trial .

Given : A study conducted at a certain college shows that​ 65% of the​ school's graduates find a job in their chosen field within a year after graduation.

i.e. p= 0.65

Sample size : n= 11

Now, the probability that 11 randomly selected graduates all find jobs in their chosen field within a year of graduating:-

$P(X)=^{11}C_{11}(0.65)^{11}(1-0.65)^{11-11}\\\\=(1)(0.65)^{11}(1)\\\\=0.00875078317401\approx0.009$

Hence, the probability that 11 randomly selected graduates all find jobs in their chosen field within a year of graduating = 0.009