Question

Northlake high scores to lunch. Soon can eat their lunch in the cafeteria or on an outside patio about 35% of students who have first lunch eat outside compare this with a percenta

Answer 1

Answer:

The proportion of second lunch students who eat outside is more than that for the first lunch students.

Step-by-step explanation:

The complete question is:

Points Northlake High School has two lunch periods. Students can eat their lunch in the cafeteria or on an outside patio. About 35% of students who have first lunch eat outside. Compare this with the percentage of second-lunch students who eat outside.

                            Eat Outside         Eat Inside          Total

First Lunch                 0.19                    0.35               0.54

Second Lunch           0.22                   0.24               0.46

Total                           0.41                    0.59               1.00

Solution:

The conditional probability of an event B given that another event A has already occurred is:

$P(B|A)=\frac{P(A\cap B)}{P(A)}$

The probability of students who have second lunch (S) and eat outside (O) is:

P (S ∩ O) = 0.22

The probability of students who have second lunch (S) is:

P (S) = 0.41

Compute the proportion of student who eats outside given they have second lunch as follows:

$P(O|S)=\frac{P(S\cap O)}{P(S)}$

            $=\frac{0.22}{0.41}\\\\=0.536583\\\\\approx 0.54$

The proportion of second lunch students who eat outside is more than that for the first lunch students.