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Can Somone help explain this to me, don't need the answers just a bit of guidance, I'm kind of lost on this one.

A consumer advocate claims that 80 percent of cable television subscribers are not satisfied with their cable service. In an attempt to justify this claim, a random sample of 20 subscribers is taken.

6.  The probability of 15 or fewer are not satisfied with the service.

7.  The probability that exactly 14 consumers are not satisfied.

8.  The probability of at least 13 consumers are not satisfied.

9.  The expected number of consumers to not be satisfied.

10. The standard deviation.
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On the assumption that the number of subscribers is quite large, the binomial distribution provides a reasonable model. –  André Nicolas Nov 3 '12 at 23:18

1 Answer 1

On the assumption that the number of subscribers is quite large, the binomial distribution provides a reasonable model.

We assume that with probability $p=0.8$, a customer is not satisfied. Let $X$ be the number of dissatisfied customers in a random sample of $n$ customers. For any integer $k$ with $0\le k\le n$, we have $$\Pr(X=k)=\binom{n}{k}p^k(1-p)^{n-k}.$$

This should be useful in answering the first three questions. For the sake of ease of computation, in 6) it may be useful to find first the probability of the complementary event that $16$ or more are not satisfied.

For the last two questions, I imagine you are expected to use standard results about the mean and variance of the binomial. Imagine we perform an experiment independently $n$ times, with probability $p$ of "success" each time. Let $X$ be the total number of successes. Then the mean of the binomially distributed random variable $X$ is $np$, and the variance of $X$ is $np(1-p)$. Recall that the standard deviation is the square root of the variance.

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