Question

the counselor picked a random sample of 160 senior scores and recorded the
information in the table below. use this data to answer questions 1 - 5.

1. what is the proportion of students that scored less than 20.8 on the act at lincoln

high school?

1. estimate the probability of a senior in the random sample scoring less than 20.8 on

the act? explain your method.

Explanation:

Step1: Find the proportion of students scoring less than 20.8

The total number of students is \(104 + 56=160\). The number of students who scored less than \(20.8\) is \(104\). The proportion \(p=\frac{\text{Number of students with score}<20.8}{\text{Total number of students}}\). So, \(p = \frac{104}{160}\).

Step2: Simplify the fraction

\(\frac{104}{160}=\frac{104\div8}{160\div8}=\frac{13}{20}=0.65\)

Answer:

1. The proportion of students at High School that scored less than \(20.8\) on the ACT is \(0.65\).
2. To estimate the probability that a senior in the random sample scoring less than \(20.8\) on the ACT, we use the relative - frequency approach. The probability \(P\) is estimated as the proportion of students in the sample with the desired outcome. Since \(104\) out of \(160\) students scored less than \(20.8\), \(P=\frac{104}{160}=0.65\).