<p>The probability of finding legionella in an electronic faucet is 15%. Legionella was found in 10 out of 20 faucets. The probability of finding legionella in 10 or more faucets is .00025.</p>
<p>Question: Does the study provide sufficient evidence that the probability of legionella bacteria growing in electronic faucets is greater than 15%?</p>
<p>The answer is yes because .00025 is really low. I don't understand that at all...Why does it matter that .00025 is low? How does that tell you that the probability is most likely higher than 15%?</p>
<p>If you did the calculator command for this, you would get 1-binomcdf(20,.15,9)=2.4838x10^-4, which is not quite .00025, so the probability must be slightly greater than 15%. For example, 1-binomcdf(20,.1501,9)=2.4978x10^-4 </p>
<p>@kevinjuan 2.4838 x 10^(-4) is pretty much .00025. The probability distribution is not continuous; you can’t obtain 9.99 or 10.01 out of 20 defective faucets.</p>
<p>The reason is that obtaining 10/20 faucets would have been extremely unlikely (P(10/20) = 0.00025) assuming that P(legionella) = 15%.</p>