Question

micah surveys a random sample of 20 band members from his school to find out how many minutes they practice their instruments each day. the results are shown in the dot plot. micah estimates that 10 students in the entire band practice more than 30 minutes each day. is this a reasonable estimate? this is not a reasonable estimate. there are? students in the sample who practice more than 30 minutes each day. there should be? 10 students in the entire band who practice more than 30 minutes each day.

Explanation:

Step1: Count students in sample

Count the number of dots (students) in the sample who practice more than 30 minutes.
From the dot - plot: \(1 + 1+4 + 6=12\) students practice more than 30 minutes in the sample.

Step2: Analyze the estimate

Since there are 12 students in the sample of 20 who practice more than 30 minutes, the proportion is \(\frac{12}{20}=\frac{3}{5}\). If we assume the entire band has a similar proportion, and Micah's estimate is 10, but the sample shows a higher number of students (12 in the sample) practicing more than 30 minutes. So Micah's estimate is not reasonable.

Answer:

There are \(12\) students in the sample who practice more than 30 minutes each day. There should be \(more\ than\) 10 students in the entire band who practice more than 30 minutes each day.