Please help me with a question on probabilities

Hello all,

Four fifths of the residents in a particular street oppose the construction of traffic lights at the end of the street. One of the residents decides to carry out a formal survey and randomly samples 20 people who live in the street. Find the probability that:

(a) Exactly 16 residents oppose the construction of the lights.

Ok, now I used binomial probabilities to solve this. (20C16) *(4/5)^16 * (1/5)^4 = 0.218

(b) 16 or more residents oppose the construction of the lights.

I'm not sure how I should solve this. Are binomial probabilities applicable?

You can use the binomial probabilities to solve this, work out P(X=16) all the way up to 20 then add those probabilities together and you will get the answer.

Or you can use cumulative binomial probability tables to work out P(X ≥ 16). If you read off 16 on your cumulative binomial probability table you will be reading P(X ≤ 16). Which is obviously wrong, you need to do 1 - P(X ≤ 15), this will give you P(X ≥ 16).

If you read it off you should get the answer as: 0.6296.

Hope I helped!

b)
P( 16 or more) = P(x=16)+P(x=17)+P(x=18)+P(x=19)+P(x=20)
Find each (you have already solved for x=16) and add:

16 0.218199
17 0.205364
18 0.136909
19 0.057646
20 0.011529
add: 0.629648

round off as desired