Final answer:
To be 95% confident the true mean birth weight of infants is within 2 ounces of the sample mean with a known population standard deviation of 5 ounces, the nurse would need to sample 25 infants.
Step-by-step explanation:
The student is interested in determining the size of a sample needed to estimate the true mean birth weight of infants within 2 ounces of the sample mean with 95% confidence when the population standard deviation is known to be 5 ounces. This problem can be solved using the formula for the sample size in a confidence interval estimation for a population mean:
Sample Size (n) = (Z*σ/E)^2
where:
- Z is the Z-score associated with the desired confidence level,
- σ (the Greek letter sigma) is the population standard deviation,
- E is the desired margin of error (the maximum difference allowed between the sample mean and the population mean).
For a 95% confidence level, the Z-score (Z*) is typically 1.96. The population standard deviation (σ) is given as 5 ounces, and the margin of error (E) is 2 ounces.
Plugging these values into the formula:
n = (1.96 * 5 / 2)^2
n = (9.8 / 2)^2
n = (4.9)^2
n = 24.01
Since the sample size must be a whole number, we would round up to the next whole number, which is 25. Thus, the nurse would need a sample of 25 infants to be 95% confident that the true mean birth weight is within 2 ounces of the sample mean.