High School

Use the given information to find the minimum sample size required to estimate an unknown population mean.

How many women must be randomly selected to estimate the mean weight of women in one age group? We want 90% confidence that the sample mean is within 3.4 lb of the population mean, and the population standard deviation is known to be 25 lb.

A) 145
B) 147
C) 208
D) 148

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.

Know more about mean here:

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