Complete the following question very neatly and clearly indicate the anwsers and

Question

Complete the following question very neatly and clearly indicate the anwsers and if you are not sure that your anwser is correct please let someone els do the problem do not skip any step and show all your work.

+-2 points DevoreStat8 5.E.047 My Notes The inside diameter of a randomly selected piston ring is a random variable with mean value 10 cm and standard deviation 0.05 cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.) 10.01) when n = 16. (a) Calculate P(9.998 X (9.99 x 10.01) = (b) How likely is it that the sample mean diameter exceeds 10.01 when n25? P(X 2 10.01) You may need to use the appropriate table in the Appendix of Tables to answer this question. Submit Answer Save Progress Practice Another Version

Explanation / Answer

Here mean is 10 and sd is 0.05

a. P(9.99<x<10.01)=P(9.99-10/(0.05/sqrt(16))<z<10.01-10/(0.05/sqrt(16))=P(-0.8<z<0.8)=P(z<0.8)-P(z<=-0.8)=0.7881-0.2119=0.5762

b. P(x>10.01)=P(z>=1)=1-P(z<1)=1-0.8413=0.1587. Here n is 25 so z=(xbar-mean)(sd/sqrt(n))=1

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