In February 2021, a survey was carried out to find the number of days 500 patients stayed at a hospital. The graph shows the cumulative frequency curve for the data collected. Use the curve to estimate (i) the median number of days, Answer ... days (ii) the interquartile range of the number of days, Answer ... days (iii) the percentage of patients who stayed more than 20 days in the hospital. Answer ... % In February 2022, the same survey was carried out again on another 500 patients with the following result shown in the box-and-whisker plot below. Make two comments comparing the number of days stayed in the hospital in February 2021 and February 2022.
Use figures to support your answer. Answer

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One patient in February 2021 was selected at random. Find the probability that the patient stayed for at most 20 days. Answer ... Two patients in February 2022 were selected at random. Find the probability that one of the patients stayed for at most 8 days while the other stayed for more than 8 days. Answer ...

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Worked solution

1. Find the number of patients who stayed for at most 8 days and more than 8 days.

From the box-and-whisker plot, the lower quartile is $8$ days.

So $25\%$ of the $500$ patients stayed for at most $8$ days.

$\text{Number at most 8 days}=\frac14\times 500=125$

$\text{Number more than 8 days}=500-125=375$

2. Calculate the probability of selecting one patient from each group in either order.

There are two possible orders:

Since the patients are selected without replacement,

$P=\frac{125}{500}\times\frac{375}{499}+\frac{375}{500}\times\frac{125}{499}$

$P=2\left(\frac{125}{500}\times\frac{375}{499}\right)$

$P=\frac{375}{998}$

Answer

$\dfrac{375}{998}$

AI analysis — may contain mistakes.

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