Question

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities.

Fifty dash sevenFifty-seven

percent of parents would give up cable television to have their​ child's education paid for. You randomly select

fivefive

parents. Find the probability that the number of parents who would give up cable television to have their​ child's education paid for is​ (a) exactly

twotwo​,

​(b) less than

fourfour​,

and​ (c) at least

threethree.

Answer 1

here this is binomial with parameter n=5 and p=0.57

a)

P(X=2)=

(nCx)px(1−p)(n-x)    =

0.2583 (please try 0.258 if required to 3 decimals)

b)

P(X<4)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.7129 (please try 0.713 if required to 3 decimals)

c)

P(X>=3)=1-P(X<=2)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.6295 (please try 0.630 if required to 3 decimals)