(a) To draw the histogram, calculate the frequency density for each class interval using the formula:

\(\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}\)

Class widths: 10, 10, 20, 20, 40

Frequency densities: \(\frac{16}{10} = 1.6\), \(\frac{54}{10} = 5.4\), \(\frac{78}{20} = 3.9\), \(\frac{32}{20} = 1.6\), \(\frac{20}{40} = 0.5\)

Draw bars with these heights on the histogram.

(b) To estimate the mean time, use the midpoints of each interval:

Midpoints: 5, 15, 30, 50, 80

Mean = \(\frac{16 \times 5 + 54 \times 15 + 78 \times 30 + 32 \times 50 + 20 \times 80}{200}\)

\(= \frac{80 + 810 + 2340 + 1600 + 1600}{200}\)

\(= \frac{6430}{200} = 32.15\)

Accept 32.2 as the answer.

(c) The greatest possible value of the interquartile range is calculated by taking a value in the upper quartile (40-60) and subtracting a value in the lower quartile (10-20):

\(Greatest possible value = 60 - 10 = 50\)