Question

A survey of the students in Lance’s school found that 58% of the respondents want the school year lengthened, while 42% think it should remain the same. The margin of error of the survey is ±10%.

According to the survey data, at least
% of students want the duration of the school year to remain unchanged, and at least
% want the school year to be lengthened.

Answer 1

Due to the margin of error of 10% I would say that then at least 48% wanted the school year lengthened and at least 32% want to keep it the same. I got these figures by subtracting the 10% from the nominal figures to give minimum figures for both.

Answer 2

According to the survey data:

at least 32% of students want the duration of the school year to remain unchanged, and

at least 48% want the school year to be lengthened.

Explanation:

Margin of error--

The margin of error is the small amount that leads to the miscalculation of some value.

We are given that:

The margin of error of the survey is ±10%.

• A survey of the students in Lance’s school found that 58% of the respondents want the school year lengthened.

Hence, due to the margin of error the percent of students who want school year to be lengthened lie between:

(58-10)% to (58+10)%

i.e. 48% to 68%.

Similarly,

• 42% think it should remain the same.

Hence, due to the margin of error the percent of students who want school year to remain same lie between:

(42-10)% to (42+10)%

i.e. 32% to 52%.