Question

Une tho standard o mal dstritution or thtdstritution to construct a 9 con idence interval tor the popula on me an Justty yor decision rester dstnbton can be In a rardom sampie of 21 mongo e institutors, the mean interest rate was 3 42% and stardid d viation was O 45% Assume the irtonost rates are rermal y distiMed Which dstribution should be used to corestruct the confidence interva? O A. Use a normal distribution because the intorest rates are normally dstributed and e is known. B. Use a t-dstnibution becase the interest rates are normally dstributed and o is known C. Use a tdistribution because it is a random ○ D. Use a normal dstbution becase n< 30 and the interest rates are normally dstrituted ○ E. Carrot use the standard normal dstnbton or the tdutbution because, is unknown, n< 30, and the ireerest rate ae not noenaly datnaaed t is a random sampie, Ơ ts urknown, and the interest rates are normally distributed Select the correct choice below and, it necessary, il in any arewer boxes to complete your choice OA. The 0% corifidence interval is O B. Neither distribution can be used to construct the confidence incerval Round to two decimal places as needed )

Answer 1

M = 3.42
t = 1.72
s_M = √(0.45²/21) = 0.1

μ = M ± t(s_M)
μ = 3.42 ± 1.72*0.1
μ = 3.42 ± 0.1694

90% CI [3.2506, 3.5894].