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It looks like you're working on a problem related to the age distribution of nurses in Great Britain during the time of Florence Nightingale (1851). Let's break down what I see from the image:

1. **Table Information**:
   - The table provides an age range, the midpoints of those age ranges, and the percentage of nurses in each range.
   - Age ranges: 20-29, 30-39, 40-49, 50-59, 60-69, 70-79, 80+.
   - Midpoints: 24.5, 34.5, 44.5, 54.5, 64.5, 74.5, 84.5.
   - Percent of nurses: 5.8%, 9.5%, 19.7%, 29.8%, 24.6%, 8.8%, 1.8%.

2. **Parts of the Problem**:
   - **(a)** You are asked to determine whether the percentages in the table represent a valid probability distribution. The answer appears to be **Yes**, the events are distinct and the probabilities sum to 1.
   - **(b)** A histogram is shown graphing the probability distribution.
   - **(c)** You're calculating the probability that a nurse was 60 years or older in 1851, and the result seems to be **0.352**.
   - **(d)** You're asked to compute the expected age \( \mu \) of a British nurse. I can't see the numerical result, but you would calculate this using the weighted average formula.
   - **(e)** You're also asked to compute the standard deviation \( \sigma \) for the ages of nurses.

Would you like help solving or verifying any specific part of this problem? For example, I can help you calculate the expected age, standard deviation, or probability.

### Next Questions:
1. Would you like to verify how to calculate the expected age \( \mu \)?
2. Would you like help with finding the probability in part (c) more explicitly?
3. Do you need assistance in creating the histogram in part (b)?
4. Would you like to walk through the calculation of standard deviation in part (e)?
5. Are you curious about the validity of the probability distribution in part (a) and why it sums to 1?

### Tip:
To calculate the expected value \( \mu \), you need to multiply each age midpoint by the corresponding percentage (converted to a decimal), then sum the results.

What was the age distribution of nurses in Great Britain during the time of Florence Nightingale?

Explore the statistical analysis of the age distribution of nurses in 1851 Great Britain, covering probability distributions, expected age calculation, and standard deviation. This analysis reflects key concepts in probability and statistics suitable for college-level students.

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