Question

the table and corresponding frequency polygon show information about the waiting times of some patients at a hospital. what fraction of patients waited for more than 7 minutes? waiting time (x minutes) 5<x≤6 6<x≤7 7<x≤8 8<x≤9 9<x≤10

Explanation:

Step1: Estimate frequencies from graph

From the frequency - polygon, assume frequencies for each interval:
For \(5 < x\leq6\), frequency \(f_1 = 2\); for \(6 < x\leq7\), frequency \(f_2 = 8\); for \(7 < x\leq8\), frequency \(f_3 = 6\); for \(8 < x\leq9\), frequency \(f_4 = 4\); for \(9 < x\leq10\), frequency \(f_5 = 2\).

Step2: Calculate total frequency

The total frequency \(N=f_1 + f_2+f_3+f_4+f_5=2 + 8+6 + 4+2=22\).

Step3: Calculate frequency of patients waiting more than 7 minutes

The frequency of patients waiting more than 7 minutes \(n=f_3+f_4+f_5=6 + 4+2 = 12\).

Step4: Calculate the fraction

The fraction of patients who waited more than 7 minutes is \(\frac{n}{N}=\frac{12}{22}=\frac{6}{11}\).

Answer:

\(\frac{6}{11}\)