Question

The customers of a music store are surveyed to determine their favorite leisure time activity. Of these, 85% said that they like to listen to music, so the store manager concludes that most people prefer to listen to music in their leisure time.

Is this a valid conclusion? Explain your ans

Answer 1

`\large\boxed{\textsf{This is a valid conclusion.}}`

Explanation:

`\textsf{\boxed{85\%} of people said that they like to listen to music in their leisure time.}`

`\large\underline{\textsf{What is a Percentage?}}`

`\textsf{A Percentage is a fraction that represents part of a total.}`

`\underline{\textsf{Example;}}`

`\textsf{35\% of people out of the total 100 enjoy dancing.}`

`\textsf{This means that} \ \tt (35)/(100) \ (35 \ out \ of \ 100)\ \textsf{people enjoy dancing.}`

`\textsf{For this problem, we are not given a total amount of people, but we are given the}`

`\textsf{percentage. We want to find out if the majority of people like to listen to music in}`

`\textsf{their leisure time.}`

`*\textsf{Note that 85\% represents that} \ \tt (85)/(100) \ (85 \ out \ of \ 100)\ \textsf{people like to listen to music in their}`

`\textsf{leisure time.}`

`\large\underline{\textsf{What does Most/Majority Mean for Our Problem?}}`

`\textsf{Majority/Most means what is more likely to happen, or what is more liked.}`

`\textsf{Mainly the same, both describe what percentage is closer to the total. Remember}`

`\textsf{that the percentage closer to 100\% , or the percentage greater than 50\% is the majority.}`

`\underline{\textsf{For our Problem;}}`

`\textsf{Because 85\% is greater than 50\%, we can conclude that the majority of people}`

`\textsf{prefer to listen to music in their leisure time.}`

`\large\boxed{\textsf{This is a valid conclusion.}}`