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

Answer:

567 people were surveyed.

Step-by-step 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:

$\frac{57.5\%-49.1\%}{2}$

$=\frac{8.4\%}{2}$

$=4.2\%.$

Let the number of people surveyed be $n.$

Now, to get the number of people surveyed:

$4.2\%=\frac{1}{\sqrt{n} }$

$\frac{4.2}{100}=\frac{1}{\sqrt{n} }$

$0.042=\frac{1}{\sqrt{n} }$

By cross multiplying we get:

$\sqrt{n}=\frac{1}{0.042}$

$\sqrt{n}=23.81$

Using square root on both sides we get:

$n=566.91.$

Approximately:

$n=567.$

Therefore, 567 people were surveyed.