Upon examining its records, a hospital computes the distribution of the number of days a patient stays at the hospital. They find that 50% of patients stayed just one day before leaving. 30% stayed two days, and 10% stayed 3 days.
a.) A patient is selected at random from the hospital's records. Keeping in mind that every patient stays at least one day, what is the chance that this patient stayed longer than 3 days? Show your work.
b.) For the hospital, the mean length of stay was 4.3 days. Thus,
A.) the mean length of stay is larger than the median.
B.) the mean length of stay is smaller than the median.
C.) the mean length of stay is the same as the median.
D.) it is impossible to tell whether the mean is larger or smaller than the median.
Pick one and explain.
That is only 90% of the patients. Did the other 10% die?
a.) To calculate the chance that a patient stayed longer than 3 days, we need to determine the percentage of patients who stayed 3 or more days out of the total number of patients.
Since we already know that 50% stayed one day, 30% stayed two days, and 10% stayed three days, we can subtract these percentages from 100 to find the remaining percentage.
Percentage of patients who stayed longer than 3 days = 100% - (50% + 30% + 10%)
= 100% - 90%
= 10%
Therefore, the chance that a randomly selected patient stayed longer than 3 days is 10%.
b.) To determine whether the mean length of stay is larger than, smaller than, or the same as the median, we need to consider the given information about the mean length of stay, which is 4.3 days.
The median represents the middle value when all lengths of stay are arranged in ascending order. In this case, since the exact quantities for each length of stay are not provided, it is not possible to determine the exact median. However, we can make some general observations based on the given percentages.
We know that 50% of patients stayed one day, 30% stayed two days, and 10% stayed three days. These values indicate a skewed distribution with a majority of patients staying for a short duration, while a smaller percentage stayed for a longer duration.
Since the mean length of stay is 4.3 days, which is larger than the lengths of stay for a significant portion of patients (1, 2, and 3 days), we can conclude that the mean is likely to be larger than the median.
Therefore, the correct answer is A.) the mean length of stay is larger than the median.