Question

The time between arrivals of 52 patients at an intensive care unit were recorded to the nearest hour. The data are shown below. (20 Marks)

Time (Hours)

[0-20)

[20-40)

[40-60)

[60-80)

[80-100)

[100-120)

[120-140)

Frequency

16

13

7

4

3

4

5

I. Construct a histogram and cumulative frequency polygon for these data.

II. Estimate the percentage of the time between arrivals of patients with less than 80 hours.

Answer 1

i.

$$\def\arraystretch{1.5} \begin{array}{c:c} Time(hours) & Cumulative\ frequency \\ \hline 0 & 0 \\ 19.5 & 16\\ 39.5 & 29\\ 59.5 & 36\\ 79.5 & 40\\ 99.5 & 43\\ 119.5 & 47\\ 139.5 & 52\\ \end{array}$$

ii.

$$P(T<80)=\dfrac{40}{52}=\dfrac{10}{13}\approx0.76923$$

$77\%$