Question

1) A NORMAL DISTRIBUTION HAS 4:47 AND 0=3 FIND THE PROBABILITY A RANDOM VARIABLE WITH THIS DISTRIBUTION WILL BE BETWGEN SO AND SS 2) A SAMPLE OF SIZE 40 is SELECTED AT RANDOM FROM A POPUUTON WITH MEAN 100 AND STANDARD DEVIA. 15. WHAT IS THE PROBABITY THAT X ComourGD FROM THIS SAMPLE IS GREATER THAN 115? 3) A SAMPLE OF SIZE 89 15 SELECTED 17 RANDOM FROM A POPULATION CONSTRUCT A 95% CONFIDENCE INTERVAL FOR THE MEAN OF THIS POPULATION GIVEN THAT THE SAMPLE MASA MGAN X = 87.2 AND A SYNDARD DEVUTON S = 5.3. 4) GIVEN TG CON FIDENCE WORVAL 1 quaslov 3 1Bove, IF 706 LOVGL OF GWFIDENCE WAS INCREASED TO 99% WOULD TE CUNONCE WYGRVAL BGGOMG LAAGGR OR SMAUER EXPLAIN YOUR ANSWER

Answer 1

1.

Given that X follows a Normal distribution with Mean = u = 47 S.D=0=3 Note that z= (x-u)/o = (x-47)/3 ---(Eq.1) follows standard Normal.

When x = 50, from (Eq.1), z = 1 When x = 55, from (Eq.1), z = 2.67 P(50<x<55)=P(1 <Z<2.67)=P(Z <2.67) - P(Z <1)=0.9962 -0.8413 = 0.1549

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