Question

The amount of coffee that people drink per day is normally distributed with a mean of 15 ounces and a standard deviation of 6 ounces. 13 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X-N b. What is the distribution of m?T-NG c. What is the probability that one randomly selected person drinks between 14 and 16 ounces of coffee per day? d. For the 13 people, find the probability that the average coffee consumption is between 14 and 16 ounces of coffee per day. e. For part d), is the assumption that the distribution is normal necessary? O Yes No f. Find the IQR for the average of 13 coffee drinkers. Q1 = ounces

Answer 1

let the amount of coffee consumed. is random variable x. (b @ x ~ N(156) we know that it xaN(0) then * ~ N(M, v so x ~ N (15, ) Viz OY X ~ N (15, 1.664) (to a decimal places) Also it x~ N(Mo) then. z- X-M N(0, 1) P ( 14 CXC16) = P114-15 X-15 (16-15 6 = P(-0.166666< Z <0.166666) calculator From 2-table p(14<x<16) = 0.13237 P(14 < X <16) =P 14-15 < 6/513 GN 6/fis P(-0.600g 25.2.0.600925) from 2-table calculator : P(14CX216) = 0.45211