Question

An article reported that what airline passengers like to do most on long flights is rest or sleep; in a survey of 3697 passengers, almost 80% did so. suppose that for a particular route the actual percentage is exactly 80%, and consider randomly selecting nine passengers. then x, the number among the selected nine who rested or slept, is a binomial random variable with n = 9 and p = 0.8. (round your answers to four decimal places.)

Answer 1

F(x,n,p)=C(n,x)p^x*(1-p)^(n-x)
n=9, p=0.8  =>
f(x,9,0.8)=C(9,x)0.8^x*(0.2)^(9-x)

The function f(x,9,0.8) is then calculated using the above formula
x f(x)
0 0.0000001 0.0000182 0.0002953 0.0027534 0.0165155 0.0660606 0.1761617 0.3019908 0.3019909 0.134218

Check Sum f(x), [x=0,9] = 1.0   ok