# Find the probability that 8 or more will feel that the system is adequate. Find the probability that exactly 8 will feel that the system is adequate.

Only 20% of the people in a large city feel that its mass transit system is adequate. If 20 persons are selected at random, find the probability that 8 or more will feel that the system is adequate. Find the probability that exactly 8 will feel that the system is adequate.

Round the answers to 3 decimal places.

The probability that 8 or more will feel that the system is adequate is X

The probability that exactly 8 will feel that the system is adequate is Y

Find X and Y

I think there is a way for my calc to do this. bionomCDF but I'm not sure how to do it

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Hint:

Let $X$ be the random variable indicating the number of people, out of 20, that feel the mass transit system is adequate. Then,

$$X \sim Bin (N, p)$$

Hence, $P(X\geq 8) = P(Bin(N, p) \geq 8 = 1 - cdf(7)$ and $P(X=8) = P ( Bin(N, p) = 8) = pdf(8)$. where $pdf, cdf$ were calculated for $Bin(N, p)$.

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I'm still kind of confused. Could you put it into simpler terms? – Joe Jan 13 '13 at 7:09
@Joe Figure out why $N$ and $p$ are supposed to be. – Calvin Lin Jan 13 '13 at 7:10
How do I find that? – Joe Jan 13 '13 at 7:13
@Joe By using your brain. Do you think $N$ is 8 or 20, or $0.20 \times 20$, or any combination of those values? Likewise, do you think $p$ is $0.20$, or $8/20$ or $20/8$, or any combination of those values? – Calvin Lin Jan 13 '13 at 7:16
yeah p would be .2 and q would be .8 so youd end up with .0894. But I'm sure there's more to it – Joe Jan 13 '13 at 7:20