solve all problems The tolerances on the diameter of a shaft are specified as 2

Question

  solve all problems

The tolerances on the diameter of a shaft are specified as 2 t0.05 in. The shafts produced by a machinist are found to have a mean value of 2.01 in and a standard deviation of 0.02 in. Find the fraction of the machined shafts that need to be discarded. Assume diameter of a shaft follows normal distribution. A firm manufactures cylindrical machine part. The diameter of the part is normally distributed. with a mean of 8.350 cm and standard deviation of 0.093 cm. A part is considered satisfactory if its diameter lies between 8.205 and 8.490 cm. what is the proportion of defective parts? The compressive strength of concrete has a mean of 2500 psi and a standard deviation of 50 psi. Find the probability that a random sample of n -5 specimens will have a sample mean strength that falls in the interval from 2490 psi to 2310 psi.

Explanation / Answer

8)

hence probability that shaft is satisfactory:

therefore P(shaft to be discarded) =1-P(shaft is satisfactory) =1-0.9759 =0.0241

9)

probability of satisfactory:

hence P(defective ) =1-0.8751=0.1249

10)

for normal distribution z score =(X-)/x here mean=       = 2.01 std deviation   == 0.020

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