Question

semester student applications (in thousands) 1 106 2 137 3 285 4 120 5 202 6 195 7 327 8 139 9 307 10 318 11 212 12 217 states base their decisions on data like this. suppose a state decides that if fewer than 200,000 students apply during 6 or more semesters, the state will make a special effort to promote university education. using this data, what is the sample proportion of semesters for which the number of student applications is less than 200,000? a 42% b 20% c there is insufficient data to answer this question

Explanation:

Step1: Count the number of semesters with applications < 200,000

From the table, semesters 1 (106), 2 (137), 4 (120), 8 (139) have applications less than 200,000. So \(n = 4\).

Step2: Calculate the total number of semesters

There are \(N=12\) semesters in total.

Step3: Calculate the sample proportion

The formula for sample proportion \(p=\frac{n}{N}\). Substituting \(n = 4\) and \(N = 12\), we get \(p=\frac{4}{12}=\frac{1}{3}\approx0.333\). But wait, let's re - check.
Wait, no! Wait, the values are in thousands. Semesters 1 (106000), 2 (137000), 4 (120000), 8 (139000) are less than 200000. So \(n = 4\), \(N = 12\). The proportion \(p=\frac{4}{12}=\frac{1}{3}\approx0.333\). But wait, no - looking at the options, maybe a miscalculation. Wait, no:
Wait, actually, let's re - count:
Semester 1: 106 (in thousands) = 106000 < 200000
Semester 2: 137 (in thousands)=137000 < 200000
Semester 3:285 (in thousands) = 285000>200000
Semester 4:120 (in thousands)=120000 < 200000
Semester 5:202 (in thousands)=202000>200000
Semester 6:195 (in thousands)=195000 < 200000
Semester 7:327 (in thousands)=327000>200000
Semester 8:139 (in thousands)=139000 < 200000
Semester 9:307 (in thousands)=307000>200000
Semester 10:318 (in thousands)=318000>200000
Semester 11:212 (in thousands)=212000>200000
Semester 12:217 (in thousands)=217000>200000

So \(n = 5\) (semesters 1,2,4,6,8) and \(N = 12\). Then \(p=\frac{5}{12}\approx0.417\approx42\%\)

Answer:

A. 42%