A population has μ = 150 and σ = 24. A random sample of n = 64 is selected. Find P(x̄ < 156).

A random sample has x̄ = 70, s = 9, and n = 16. The population standard deviation is unknown. Find the 95% confidence interval for μ.

For a population with μ = 40, σ = 8, and samples of size n = 64, identify the mean and standard deviation of the sampling distribution of x̄.

The population proportion is p = 0.40. For n = 200, find P(0.36 < p̂ < 0.45).

X is normally distributed with μ = 100 and σ = 15. Find the value corresponding to the 95th percentile.

A random sample has x̄ = 120, s = 18, and n = 30. The population standard deviation is unknown. Find the 99% confidence interval for μ.

A sample has x = 120 successes out of n = 200. Find the margin of error for a 99% confidence interval for p.

A sample has x̄ = 55, population σ = 8, and n = 49. Find the 95% confidence interval for μ.

A sample has x̄ = 80, population σ = 12, and n = 36. Find the 95% confidence interval for μ.

In a random sample of n = 80, x = 48 subjects have the characteristic of interest. Find the 90% confidence interval for the population proportion p.