Question

The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 8.1 8.1 ounces and standard deviation 0.11 0.11 ounces. (a) What is the probability that the average weight of a bar in a simple random sample of four of these chocolate bars is between 8 8 and 8.2 8.2 ounces? (b) For a simple random sample of four of these chocolate bars, what is the level L L such that there is a 1 1 % chance that the average weight is less than L L ?

Answer 1

et x he the autual weight of 9-02 choco lates bars produced by certain muchine HN(1, -0-11 ) a) The probablity that the avceage wesght df a bar simple random sample of four is betw cen given by in a qnd . 2 o 2 P(8S8-2) - Pl8- Y 8.2-4 8-8 <Z< 8.2 - 8.) P V4 O. J -O O 1 OOSS O.O55 P181 S S 1.81 18-1-32d (i8-5 z)d by using Po.9649 0 035) 2 table 0.9298 P[8 SR2] - 0.9298

) The vale of 'L such tat there is % Chane that the average weigh is Tss than 2 obtaind by P L0.01 スー 0.0 - 1-2-721d T0.e I8-7 2Jd |0.D using inveesc (10.0)d Df funchon both side L- 81 O-OS5 L-8.1 2 tab le OO55-2.33 eon L-81-2:33x O 0 S5 I2S1821.0-- 1E L 797185 -. Thu value df L is 797, such tha / PC3 7.97=