please anwser all parts. thank you 8. The diameters of the metal washors produce

Question

please anwser all parts. thank you

8. The diameters of the metal washors produced by an automatic screw chine are normally distributed with a mean of 1.25 inches and a standar deviation of 10 inch. (12 POINTS) What is the probability that a random sample of a washers will have a mean diameter larger than 1.30 inches? What is the probability that a random sample of 4 washers will have a mean diameter smaller than 110 inch? is the probability that a random sample of 4 washers will have a mean diameter between 1.15 and 1.35 inches?

Explanation / Answer

Mean is 1.25 and s is 0.1

standard error SE is s/sqrt(N)=0.1/sqrt(10)=0.1/2=0.05

a) P(xbar>1.3)=P(z>(1.3-1.25)/0.05)=P(z>1) or 1-P(z<1), from normal distribution table we get 1-0.8413=0.1587

b) P(xbar<1.1)=P(z<(1.1-1.25)/0.05)=P(z<-3)=1-P(Z<3) =1-0.9987=0.0013

c) P(1.15<x<1.35)=P((1.15-1.25)/0.05<z<(1.35-1.25)/0.05)=P(-2<z<2), from normal distribution we get 2*P(z<2)-1 or 2*0.9772-1=0.9544

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