Question

2e. unit 2 review
name

1. given the two - way table that shows the number of hours using a cell phone versus the number of hours sleeping, complete the table by adding a total row and total column.

cell phone use →	< 5 hours sleep	5 - 7 hours sleep	> 7 hours sleep	total
2 - 4 hours	9	14	6
4+ hours	18	12	3
total

use the table above to answer the following questions.
a. if a student is chosen at random, what is the probability the student sleeps more than 7 hours?
b. what is the probability the student sleeps 5 - 7 hours and uses their phone 2 - 4 hours?
c. given that a student sleeps more than 7 hours, what is the probability they use their phone 0 - 2 hours?
d. given that a student sleeps less than 5 hours, what is the probability they use their phone 4+ hours?
e. what is the probability a student uses their phone more than 2 hours per day?

Explanation:

Step1: Complete the two - way table

First, calculate the total for each row and column.

For the row "0 - 2 hours" of cell phone use:
Total = 4 ( < 5 Hours Sleep) + 8 (5 - 7 Hours Sleep) + 10 (> 7 Hours Sleep) = 22

For the row "2 - 4 hours" of cell phone use:
Total = 9 ( < 5 Hours Sleep) + 14 (5 - 7 Hours Sleep) + 6 (> 7 Hours Sleep) = 29

For the row "4 + hours" of cell phone use:
Total = 18 ( < 5 Hours Sleep) + 12 (5 - 7 Hours Sleep) + 3 (> 7 Hours Sleep) = 33

For the column "< 5 Hours Sleep":
Total = 4 + 9 + 18 = 31

For the column "5 - 7 Hours Sleep":
Total = 8 + 14 + 12 = 34

For the column "> 7 Hours Sleep":
Total = 10 + 6 + 3 = 19

For the grand total (total number of students):
Grand Total = 31+34 + 19=84 (or 22 + 29+33 = 84)

Now the completed table is:

Cell Phone Use→	< 5 Hours Sleep	5 - 7 Hours Sleep	> 7 Hours Sleep	Total
2 - 4 hours	9	14	6	29
4 + hours	18	12	3	33
Total	31	34	19	84

Part a: Probability student sleeps more than 7 hours

The number of students who sleep more than 7 hours is the total of the "> 7 Hours Sleep" column, which is 19. The total number of students is 84.

Probability \( P=\frac{\text{Number of students who sleep > 7 hours}}{\text{Total number of students}}=\frac{19}{84}\approx0.226 \)

Part b: Probability student sleeps 5 - 7 hours and uses phone 2 - 4 hours

The number of students who sleep 5 - 7 hours and use phone 2 - 4 hours is 14. The total number of students is 84.

Probability \( P = \frac{14}{84}=\frac{1}{6}\approx0.167 \)

Part c: Conditional probability (sleeps > 7 hours, use phone 0 - 2 hours)

The formula for conditional probability is \( P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{n(A\cap B)}{n(B)} \)

Here, \( A \): use phone 0 - 2 hours, \( B \): sleep > 7 hours.

\( n(A\cap B)=10 \) (number of students who sleep > 7 hours and use phone 0 - 2 hours), \( n(B) = 19 \) (number of students who sleep > 7 hours)

Probability \( P=\frac{10}{19}\approx0.526 \)

Part d: Conditional probability (sleeps < 5 hours, use phone 4 + hours)

Let \( A \): use phone 4 + hours, \( B \): sleep < 5 hours.

\( n(A\cap B)=18 \), \( n(B)=31 \)

Probability \( P=\frac{18}{31}\approx0.581 \)

Part e: Probability student uses phone more than 2 hours

Students who use phone more than 2 hours are in the "2 - 4 hours" and "4 + hours" rows.

Number of students who use phone more than 2 hours: \( 29 + 33=62 \)

Total number of students: 84

Probability \( P=\frac{62}{84}=\frac{31}{42}\approx0.738 \)

Answer:

s:
a. \(\frac{19}{84}\) (or approximately \(0.226\))
b. \(\frac{1}{6}\) (or approximately \(0.167\))
c. \(\frac{10}{19}\) (or approximately \(0.526\))
d. \(\frac{18}{31}\) (or approximately \(0.581\))
e. \(\frac{31}{42}\) (or approximately \(0.738\))