(a) Plot the cumulative frequency graph using the points: (20, 32), (30, 66), (35, 112), (40, 178), (50, 228), (60, 250). Ensure the graph is smooth and passes through these points.

(b) To find the 60th percentile, locate 150 on the cumulative frequency axis and find the corresponding time on the graph. The estimated time is approximately 38 minutes.

(c) Calculate the standard deviation using the formula for variance:

First, find the midpoints of each class interval: 10, 25, 32.5, 37.5, 45, 55.

Use the formula for variance:

\(\text{Variance} = \frac{1}{250} \left( 32 \times 10^2 + 34 \times 25^2 + 46 \times 32.5^2 + 66 \times 37.5^2 + 50 \times 45^2 + 22 \times 55^2 \right) - 34.4^2\)

\(= \frac{333650}{250} - 34.4^2 = 151.24\)

The standard deviation is \(\sqrt{151.24} \approx 12.3\) minutes.