Chapter 12.7, Problem 25P

There are 250 freshmen at Central High School. You survey 50 randomly selected freshmen and find that 35 plan to go to the school party on Friday. How many freshmen are likely to be at the party?

To determine

Find the number of freshmen that are likely to be at the party.

Answer to Problem 25P

175

Explanation of Solution

Given:

There are 250 freshmen at Central High School.You survey 50 randomly selected freshmen and find that 35 plan to go to the school party on Friday.

Formula Used :

  $\text{P(E) = }\frac{\text{number of favourable outcomes of E}}{\text{total number of outcomes}}$

Calculation:

Number of freshmen that plan to go to the party = 35

Total number of freshmen selected for survey = 50

  $P(\text{freshmen at party)=}\frac{\text{favourable outcomes}}{total\text{ number of outcomes}}=\frac{35}{50}=\frac{7}{10}$

But in actual , the total number of freshmen at Central High School = 250.

So, the number of freshmen likely to be present at the party = $\frac{7}{10}\times 250=175$ (since in the survey, 50 freshmen were considered)