Question

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Suppose we have the following information. Note: In 1851 there were 25,466 nurses in Great Britain. Age range (yr) 20-29 30-39 40-49 50-59 60-69 70-79 80+ Midpoint x 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.9% 9.8% 19.1% 29.2% 25.1% 9.4% 1.5% (a) Using the age midpoints x and the percent of nurses, do we have a valid probability distribution? Explain. Yes. The events are distinct and the probabilities sum to 1. Yes. The events are distinct and the probabilities do not sum to 1. No. The events are indistinct and the probabilities sum to 1. No. The events are indistinct and the probabilities do not sum to 1. (b) Use a histogram to graph the probability distribution in part (a). Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (c) Find the probability that a British nurse selected at random in 1851 would be 60 years of age or older. (Round your answer to three decimal places.) (d) Compute the expected age μ of a British nurse contemporary to Florence Nightingale. (Round your answer to two decimal places.) yr (e) Compute the standard deviation σ for ages of nurses shown in the distribution. (Round your answer to two decimal places.) yr

Answer 1

The age distribution of nurses in Great Britain at the time of Florence Nightingale was a valid probability distribution.

Step-by-step explanation:

The age distribution of nurses in Great Britain at the time of Florence Nightingale can be determined using the provided information. The age range was divided into different categories with corresponding percentages. To determine if this is a valid probability distribution, we need to check if the events are distinct and if the probabilities sum to 1.

If the events are distinct, it means that each category is mutually exclusive and there is no overlap. In this case, the events are distinct because a nurse can only belong to one age category.

To check if the probabilities sum to 1, we add up the percentages and see if the total is equal to 1. Adding up the percentages, we get:

5.9% + 9.8% + 19.1% + 29.2% + 25.1% + 9.4% + 1.5% = 100%

Since the percentages sum to 100%, we have a valid probability distribution.