Use the standard normal distribution or the t-distribution

Last updated: 7/22/2022

Use the standard normal distribution or the t-distribution to construct a 90% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 17 mortgage institutions, the mean interest rate was 3.45% and the standard deviation was 0.38%. Assume the interest rates are normally distributed. Which distribution should be used to construct the confidence interval? A. Use a normal distribution because n∠30 and the interest rates are normally distributed. B. Use a normal distribution because the interest rates are normally distributed and σ is known. C. Use a t-distribution because it is a random sample, σ is unknown, and the interest rates are normally distributed. D. Use a t-distribution because the interest rates are normally distributed and σ is known. E. Cannot use the standard normal distribution or the t-distribution because σ is unknown, n<30, and the interest rates are not normally distributed.