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Answer :
The minimum sample size required to estimate an unknown population mean is 148. So, the correct option is D) 148.
To find the minimum sample size required to estimate an unknown population mean with 90% confidence, within 3.4 lb of the population mean, and a population standard deviation of 25 lb, follow these steps:
1. Identify the given values:
- Confidence level = 90%
- Margin of error (E) = 3.4 lb
- Population standard deviation (σ) = 25 lb
2. Find the corresponding z-score for the 90% confidence level. Using a standard normal distribution table or calculator, the z-score is 1.645.
3. Use the formula to find the sample size (n):
n = (z * σ / E)^2
n = (1.645 * 25 / 3.4)^2
4. Calculate the sample size:
n ≈ 147.267
Since we cannot have a fraction of a person, round up to the nearest whole number to ensure the required confidence level.
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