3. after many studies, a researcher finds that the probability that a word - recognition program correctly…
3. after many studies, a researcher finds that the probability that a word - recognition program correctly interprets a hand - written word is $\frac{9}{10}$. how many words out of 40 would the researcher expect the program to correctly interpret?
Answer
Explanation:
Step1: Recall the expected - value formula
The expected - value formula for a binomial - like situation is $E(X)=n\times p$, where $n$ is the number of trials and $p$ is the probability of success in a single trial. Here, $n = 40$ (the number of words) and $p=\frac{9}{10}$ (the probability of correctly interpreting a single word).
Step2: Calculate the expected number of correctly - interpreted words
$E(X)=40\times\frac{9}{10}$. We know that $40\times\frac{9}{10}=\frac{40\times9}{10}$. $40\div10 = 4$, and $4\times9=36$.
Answer:
36