# Of the 232 airports available for public use in Themeliville, 121 are paved and lighted. For a simple random sample of 50, what is the probability that between 27 and 31 of the airports in the sample will be paved and lighted?

Aug 18, 2016

$39.17$

#### Explanation:

so we have the probability of being lighted as

$p \left(L\right) = \frac{121}{232}$

this can be modeled using the binomial cumulative distribution thus

p(27<=L<=31) = sum_(k=27)^31( ""_nC_k) p(L)^k (1-p(L))^(n-k) where $n = 50$

$p \left(27 \le L \le 31\right) = 39.17$