10. a survey asked 6 random people about their eyes. of those surveyed, 2 of them reported having blue eyes…
10. a survey asked 6 random people about their eyes. of those surveyed, 2 of them reported having blue eyes. if 48 other random people were given the same survey, how many of them would you expect to also have blue eyes?
Answer
Explanation:
Step1: Calculate the proportion of blue - eyed people in the first survey
The proportion $p$ of blue - eyed people in the first survey of $n = 6$ people with $x = 2$ blue - eyed people is $p=\frac{x}{n}=\frac{2}{6}=\frac{1}{3}$.
Step2: Use the proportion to estimate the number of blue - eyed people in the second survey
We have a new sample of $N = 48$ people. Let the expected number of blue - eyed people be $X$. Using the proportion from Step 1, we have $X = p\times N$. Substituting $p=\frac{1}{3}$ and $N = 48$, we get $X=\frac{1}{3}\times48 = 16$.
Answer:
16