12. | History: Florence Nightingale What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following infor- mation (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Age range (yr) Midpoint x Percent of nurses 20-29 30-39 40-49 24.5 34.5 44.5 50-59 60-69 70-79 54.5 64.5 74.5 80+ 84.5 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8% (a) Using the age midpoints x and the percent of nurses, do we have a valid probability distribution? Explain. (b) Use a histogram to graph the probability distribution of part (a). (c) Find the probability that a British nurse selected at random in 1851 was 60 years of age or older. (d) Compute the expected age μ of a British nurse contemporary to Florence Nightingale. (e) Compute the standard deviation o for ages of nurses shown in the distribution.
12. | History: Florence Nightingale What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following infor- mation (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Age range (yr) Midpoint x Percent of nurses 20-29 30-39 40-49 24.5 34.5 44.5 50-59 60-69 70-79 54.5 64.5 74.5 80+ 84.5 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8% (a) Using the age midpoints x and the percent of nurses, do we have a valid probability distribution? Explain. (b) Use a histogram to graph the probability distribution of part (a). (c) Find the probability that a British nurse selected at random in 1851 was 60 years of age or older. (d) Compute the expected age μ of a British nurse contemporary to Florence Nightingale. (e) Compute the standard deviation o for ages of nurses shown in the distribution.
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Please answer number 12. Make sure to show work!! Answer all parts!!
Transcribed Image Text:### History: Florence Nightingale
**What was the age distribution of nurses in Great Britain at the time of Florence Nightingale?** Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text *Notes on Nursing*, by Florence Nightingale). **Note:** In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants.
#### Age Distribution of Nurses in 1851:
| 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 | 5.7% | 9.7% | 19.5% | 29.2% | 25.0% | 9.1% | 1.8%|
### Exercises:
(a) **Using the age midpoints \( x \) and the percent of nurses, do we have a valid probability distribution?** Explain.
(b) **Use a histogram to graph the probability distribution of part (a).**
(c) **Find the probability that a British nurse selected at random in 1851 was 60 years of age or older.**
(d) **Compute the expected age \( \mu \) of a British nurse contemporary to Florence Nightingale.**
(e) **Compute the standard deviation \( \sigma \) for ages of nurses shown in the distribution.**
### Explanation of Graph/Diagram:
- **Histogram:**
- A histogram displays the age distribution of nurses using the midpoints \( x \) as the x-axis values and the percent of nurses for each age range as the y-axis values.
- Each bar in the histogram corresponds to an age range (20–29, 30–39, etc.). The height of each bar represents the percentage of nurses in that age range.
These data and exercises provide historical insights into the age demographics of British nurses during the mid-19th century, reflecting the population's workforce
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