7. (6 points) A pistonis paced insid a yinder. The clearane is the distane betwe

Question

7. (6 points) A pistonis paced insid a yinder. The clearane is the distane betwen the edge of the piston and the wall of the cylinder and is equal to one-half the difference between the cylinder diameter and the piston diameter. Assume the piston diameter has a mean of 80.85 cm with a standard deviation of 0.02 cm. Assume the cylinder diameter has a mean of 80.95 cm with a standard deviation of 0.03 cm. Find the mean clearance. Assuming that the piston and cylinder are chosen independently, find the standard deviation of the clearance.

Explanation / Answer

as clerance A =(X-Y)/2 ; where X =cylinder diamter and Y=piston diameter

1)mean clearance =(mean cylinder diamter-mean piston diameter)/2=(80.95-80.85)/2 =0.05

2)

std deviation of clearance =(Var(X)+Var(Y))1/2/2 =(0.032+0.022)1/2/2 =0.018

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