A manager samples the receipts of every fifth person who goes through the line. Out of 50 people, 4 had a mispriced item. If 600 people go to this store each day, how many people would you expect to have a mispriced item?
THANK YOU!
you say
Out of 50 people
is that 50 sampled, or 50 total, of which 10 were sampled?
To find out how many people you would expect to have a mispriced item, we can use proportions based on the given information.
First, let's figure out how many people are being sampled. We know that the manager samples every fifth person, and out of 50 people, 4 had a mispriced item. This means that 4 out of 50 people were sampled.
To calculate the proportion of people who had a mispriced item in the sample, we can divide the number of sampled people with mispriced items by the total number of sampled people:
Proportion of people with mispriced items = Number of sampled people with mispriced items / Total number of sampled people
Proportion of people with mispriced items = 4 / 50
Next, we can determine the proportion of people with mispriced items in the entire population by considering the proportion of sampled people with mispriced items. Since the manager samples every fifth person, we can assume that the proportion of people with mispriced items in the entire population is the same as in the sample.
Now, let's calculate the proportion of people with mispriced items in the entire population:
Proportion of people with mispriced items in population = Proportion of people with mispriced items in the sample / Sampling rate
Proportion of people with mispriced items in population = 4 / 50 / (1/5)
Finally, to find the number of people expected to have a mispriced item out of 600 daily customers, we can multiply the proportion by the total population:
Number of people expected to have a mispriced item = Proportion of people with mispriced items in population * Total population
Number of people expected to have a mispriced item = (4 / 50 / (1/5)) * 600
By calculating the expression above, you will be able to find the number of people you would expect to have a mispriced item out of 600 daily customers.