Final answer:
To be 90% confident that the sample mean age is within 2 years of the true population mean age, 217 Foothill College students must be surveyed.
Step-by-step explanation:
In order to determine how many randomly selected Foothill College students must be surveyed to be 90% confident that the sample mean age is within 2 years of the true population mean age, we can use the formula for the confidence interval:
sample mean ± (critical value) × (population standard deviation) / √(sample size)
Since the critical value for a 90% confidence level is approximately 1.645, we can plug in the given values to find the sample size:
2 = 1.645 × 15 / √(sample size)
Solving for the sample size, we get:
sqrt(sample size) = 1.645 × 15 / 2
sample size = (1.645 × 15 / 2)^2 = 217