# When σ is unknown and the sample is of size n\geq30, there are two methods for computing confidence intervals for μ. Method1:Method1: Use the Student'

When σ is unknown and the sample is of size $n\ge 30$, there are two methods for computing confidence intervals for μ. Method1:Method1: Use the Student's t distribution with d.f. = n - 1. Method2:Method2: When $n\ge 30$, use the sample standard deviation s as an estimate for σ,σ, and then use the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. Compute 90%, 95%, and 99% confidence intervals for μμ using Method 2 with the standard normal distribution. Use s as an estimate for σσ. Round endpoints to two digits after the decimal.

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90%: 43.6341 to 46.7659
95%: 43.3343 to 47.0657
99%: 42.7441 to 47.6559