Question 1045183
a. A trial would be determining if an element of the sample has diabetes.  A success would be positive for diabetes, while a failure would be negative for diabetes. (Success rate is 0.22, while failure rate is 0.78.)

b. What is the probability that all 10 of the people have diabetes. 
{{{0.22^10 = 0.0000002656}}}, to four significant figures.


c. What is the probability that none of the 10 have diabetes?
 {{{0.78^10 = 0.08336}}}, to four significant figures.


d. What would be the average or expected amount of people with diabetes out of a sample of 10 people from this population?
{{{np = 10*0.22 = 2.2}}}, or simply 2 people on the average.


e. What is the probability that at least three of them have diabetes? 
{{{1 - p(0)- p(1) - p(2) = 1 - 0.08336 - 10C1*0.78^9*0.22^1 - 10C2*0.78^8*0.22^2 = 0.383}}} to three significant figures.


f. What is the probability that no more that two of them have diabetes? 
{{{p(0) + p(1) + p(2) = 0.08336 + 10C1*0.78^9*0.22^1 + 10C2*0.78^8*0.22^2 = 0.617}}} to three significant figures.