Question

The results of a poll show that the percent of people who want a new restaurant is in the interval (24%, 38%) . There are 112,483 people in the city.
What is the interval for the number of people who are likely to want this restaurant in their city?



Round to the nearest person.

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( , )

Answer 1

The percent of people that want a restaurant is between 24% and 38%. Since the interval is in rounded parenthesis ( ) versus square brackets [ ] we know that it is neither 24% or 38% but somewhere in between. I say this only to remind you that in our answer we have to use rounded parenthesis as well and this is the reason why.

Since there are 112,483 people we need to find 24% of that number and 38% of that number. Recall that percent means "out of 100" so 24% is $\frac{24}{100} =.24$. To find 24% of 112,483 multiply (.24)(112,483) = 26,995.92 or 26,996 when rounded to the nearest person (we can't have .92 of a person anyway).

To find 38% of 112483 we multiply (.38)(112483) = 42,743.54 or 42,744 when rounded to the nearest person.

Thus, the interval for the number of people who want the restaurant is (26996, 42744).