Question

A survey claims that the percent of an entire population that agrees with redeveloping the city park is likely between 49.1% and 57.5%. The remainder of the people in the survey were against redevelopment. How many people were surveyed?

Answer 1

567 people were surveyed.

Explanation:

Given:

A survey claims that the percent of an entire population that agrees with redeveloping the city park is likely between 49.1% and 57.5%.

Now, to find total people who were surveyed.

According to survey percent of population agrees between = 49.1% to 57.5%.

So, we need to find the error of margin:

`(57.5\%-49.1\%)/(2)`

`=(8.4\%)/(2)`

`=4.2\%.`

Let the number of people surveyed be
`n.`

Now, to get the number of people surveyed:

`4.2\%=(1)/(√(n) )`

`(4.2)/(100)=(1)/(√(n) )`

`0.042=(1)/(√(n) )`

By cross multiplying we get:

`√(n)=(1)/(0.042)`

`√(n)=23.81`

Using square root on both sides we get:

`n=566.91.`

Approximately:

`n=567.`

Therefore, 567 people were surveyed.