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WSUIT Help Use the standard normal distribution or the distribution to construct a 95% 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 13 mortgage institutions, the mean interest rate was 3.56% and the standard deviation was 0.37%. Assume the interest rates are normally distributed Which distribution should be used to construct the confidence interval? O A. Use a t-distribution because it is a random sample, is unknown, and the interest rates are normally distributed O B. Use a normal distribution because the interest rates are normally distributed and is known. O C. Use a normal distribution because n< 30 and the interest rates are normally distributed OD. Use at distribution because the interest rates are normally distributed and is known O E. Cannot use the standard normal distribution or the t-distribution because o is unknown, n < 30, and the interest rates are not normally distributed

Answer 1

Here we have, n=13 degree of freedom (df) = n1213-1212 Q = 3.56 S = 0.37 use t-distribution because the interest rates are normally distributed and o is known. The correct option- At 95% confidence interval do 10.9520.05 aalea 0.025 Housticas 10.025,12 = 2.179 950. Confidence interval for population mean EX + Beristicas * = 3.56 + 2.179* 0.37 53.56 0.2236 V13 - 3.3344, 3.7836

= 3.334, 3784 Round to three decimal places