A manager samples the receipts of every fifth person who goes through the line. Out of 50 people, 5 had a mispriced item. If 950 people go to this store each day, how many people would you expect to have a mispriced item?
Same type of question as this one:
https://www.jiskha.com/questions/1779037/Part-of-the-population-of-4-750-elk-at-a-wildlife-preserve-is-infected-with-a-parasite
Follow the same steps I used in solving it.
To answer this question, we'll first calculate the proportion of people who had a mispriced item from the sample. Then we'll use that proportion to estimate the number of people who would have a mispriced item in the entire population.
Step 1: Calculate the proportion of people who had a mispriced item in the sample.
Since the manager samples every fifth person, out of 50 people, 1/5 of them were sampled, which is 10 people. Among these 10 people, 5 had a mispriced item.
Proportion of people with mispriced items in the sample = (Number of people with mispriced items in the sample) / (Total number of sampled people)
= 5 / 10
= 0.5 (or 50%)
Step 2: Estimate the number of people who would have a mispriced item in the entire population.
To estimate the number of people who would have a mispriced item in the entire population, we assume that the proportion of people with mispriced items in the sample holds true for the entire population.
Estimated number of people with mispriced items = (Estimated proportion of people with mispriced items) * (Total population)
= 0.5 * 950
= 475
Therefore, we would expect around 475 people to have a mispriced item out of the 950 people who go to the store each day.