Question

1. a high school principal surveys 480 high school seniors about their graduation plans. when the survey results were examined, the following was observed: 100 students said they were undecided about their graduation plans 132 students said they would attend a two - year college 185 students said they would attend a four - year college 63 students said they would not attend college and would immediately enter the workforce if 20% of the students who said they would be attending a four - year college and 10% of the students who said they were undecided end up attending a two - year college, along with the 132 students who originally said they would be attending a two - year college, what proportion of the 480 surveyed students actually ended up attending a two - year college? round your final answer to three decimal places.

Explanation:

Step1: Calculate the number of students from four - year college plan who end up in two - year college

The number of students who originally planned to attend a four - year college is \(185\). \(20\%\) of them end up attending a two - year college. So the number is \(0.2\times185 = 37\).

Step2: Calculate the number of students from undecided who end up in two - year college

The number of undecided students is \(100\). \(10\%\) of them end up attending a two - year college. So the number is \(0.1\times100=10\).

Step3: Calculate the total number of students attending two - year college

The original number of students planning to attend a two - year college is \(132\). Add the students from four - year plan (\(37\)) and undecided (\(10\)). So the total is \(132 + 37+10=179\).

Step4: Calculate the proportion

The proportion is \(\frac{179}{480}\approx0.373\).

Answer:

\(0.373\)