Final answer:
The minimum sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is 237.
Step-by-step explanation:
To calculate the minimum sample size needed to estimate a population mean within a certain margin of error, we can use the formula:
n = (Z * σ / E)^2
Where:
- n is the sample size
- Z is the z-score corresponding to the desired level of confidence (for a 95% confidence level, Z = 1.96)
- σ is the population standard deviation
- E is the margin of error (in this case, 2 units)
Plug in the given values:
n = (1.96 * 8 / 2)^2
n = 15.36^2
n ≈ 236.09
Since the sample size cannot be a decimal, round up to the nearest whole number:
n = 237
Therefore, the minimum sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is 237.