Final answer:
To estimate a population mean within 1 with 90% confidence, a sample size of approximately 17 is necessary.
Step-by-step explanation:
To determine the sample size necessary to estimate a population mean to within 1 with 90% confidence given a known population standard deviation of 10, we can use the formula:
n = (Z * σ) / E
Where:
- n is the sample size
- Z is the z-score corresponding to the desired confidence level (in this case, 90% corresponds to a z-score of about 1.645)
- σ is the population standard deviation
- E is the desired margin of error (in this case, 1)
Plugging in the values, we get:
n = (1.645 * 10) / 1 = 16.45
Therefore, a sample size of approximately 17 would be necessary.