Answer to Question #284474 in Statistics and Probability for Sumit

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.

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

$77\%$