Question

the two - way frequency table below shows data on grade level and method of traveling to school for the students at central high school.which of the following statements about the students at central high school is true?choose 1 answer:a a 10th grade student is more likely to travel by bike than by car.b less than \\( \frac { 1 } { 2 } \\) of the 11th grade students travel by car.c 11th grade students are more likely than 9th grade students to travel by bike.d there are more students in 11th grade than in any other single grade.

Explanation:

Step1: Analyze option A

For \(10^{th}\) grade students, number of students traveling by bike is \(17\) and by car is \(24\). Since \(17<24\), a \(10^{th}\) grade student is less likely to travel by bike than by car.

Step2: Analyze option B

For \(11^{th}\) grade students, total number of \(11^{th}\) grade students is \(139\), number of students traveling by car is \(99\). \(\frac{99}{139}\approx0.71> \frac{1}{2} = 0.5\)

Step3: Analyze option C

For \(9^{th}\) grade students, probability of traveling by bike \(P_9=\frac{20}{51}\approx0.39\). For \(11^{th}\) grade students, probability of traveling by bike \(P_{11}=\frac{27}{139}\approx0.19\). Since \(0.39 > 0.19\), \(9^{th}\) grade students are more likely to travel by bike than \(11^{th}\) grade students.

Step4: Analyze option D

Number of \(9^{th}\) grade students \(n_9 = 51\), \(10^{th}\) grade students \(n_{10}=46\), \(11^{th}\) grade students \(n_{11}=139\), \(12^{th}\) grade students \(n_{12}=44\). Since \(139>51\), \(139 > 46\) and \(139>44\)

Answer:

D. There are more students in \(11^{th}\) grade than in any other single grade.