(Solved): Jse the standard normal distribution or the t-distribution to construct a \( 90 \% \) confidence in ...

Jse the standard normal distribution or the t-distribution to construct a \( 90 \% \) confidence interval for the populabion mean. Justify your decision. If necher distribution can be used, explain why. nterpred the results. n a random sample of 59 mortgage institutions, the mean interest rate was \( 3.62 \% \) and the standord deviation was \( 0.47 \% \). Assume the inserest rates are normally distributed Which distribution should be used to construct the confidence intervar? A. Use a idistribution because the interest rates are normally distributed and a is known. B. Uso a normal distribution because \( n<30 \) and the interest rotes are noimally distributed C. Uve a t-distribution because it is a random sample. \( \sigma \) is unknown, and the interest tates are normally distrouted. D. Use a normal distifition because the interest rates are normally distributed and \( a \) is known E. Cannot use the standard nocmal distibution or the t-distribulion becouse \( \sigma \) is unknown, \( n<30 \), and the interest rates are not norrnally diatributed. Select the conrect choice below and, it necessary, fil in any answer boxes to complote your choice. A. The \( 90 \% \) considence interval is: (RRound to two decimel places as needed.) B. Nehher ditritulion can be used to corstruct the confidence interval: Interpret the tesults, Choose the correct answer below. A. If a large sample of insilitutions are taken approximately \( 90 \% \) of them wili have an interest rate between the bounds of the contidence interval. B. With 900 confidence, it cas be said that the population moan inserest rate is between the beunds of the confidence interval. C. It can be said that \( 90 \% \) of ksilitutions have an interest rate besween the bounds of the confidence interval. D. Neither ditribution can be used to construct the confdence interval.