Question

Suppose the total snowfalls per year in a city are normally distributed. If the population standard deviation is 13 inches, what minimum sample size is needed to be 95% confident that the sample mean is within 4 inches of the true population mean?

Answer 1

To determine the minimum sample size needed to be 95% confident that the sample mean is within 4 inches of the true population mean, we can use the formula for sample size calculation. Substituting the given values into the formula, we find that a minimum sample size of 52 is needed.

Step-by-step explanation:

To determine the minimum sample size needed to be 95% confident that the sample mean is within 4 inches of the true population mean, we can use the formula for sample size calculation:

n = (Z * σ / E)²

Where:

• n is the required sample size
• Z is the z-score corresponding to the desired confidence level, which is 1.96 for a 95% confidence level
• σ is the population standard deviation, which is given as 13 inches
• E is the desired margin of error, which is 4 inches

Substituting the given values into the formula:

n = (1.96 * 13 / 4)² = 7.2256² ≈ 52

Therefore, a minimum sample size of 52 is needed to be 95% confident that the sample mean is within 4 inches of the true population mean.