Question

Given a normal population whose mean is 530 and whose standard deviation is 68, find each of the following:

A. The probability that a random sample of 3 has a mean between 541 and 557.
Probability =

B. The probability that a random sample of 14 has a mean between 541 and 557.
Probability =

C. The probability that a random sample of 29 has a mean between 541 and 557.
Probability =

Answer 1

mean is 530 and SD is 68

a) P(541<x<557)=P((541-530)/(68/sqrt(3))<z<((557-530)/(68/sqrt(3)) =P(0.28<z<0.69)= P(z<0.69)-P(z<0.28) from normal distribution table we get 0.7549-0.6103=0.1446

b) P((541-530)/(68/sqrt(14))<z<((557-530)/(68/sqrt(14))= P(0.61<z<1.49)=P(z<1.49)-P(z<0.61)=0.9319-0.7291=0.2028

c) P((541-530)/(68/sqrt(29))<z<((557-530)/(68/sqrt(29))=P(0.87<z<2.14)=P(z<2.14)-P(z<0.87)= 0.9838-0.8078=0.176