Question

Problem 2.(15 pts) A student in the ME 345 lab makes 100 thickness measurements of an aluminum bar and finds a mean thickness of 32.36 mm with a sample standard deviation of 0.55 mm. Assuming that errors are due to random processes, how many of the readings are expected to be greater than 33.0 mm? Show the interpolation in the table for full credirt.

All information needed is in the picture above.

Answer 1

Let X is the thickness measurements of an aluminum bar and which follows normal distribution.

Give that µ = 32.36 and σ=0.55 and x=33.0

  

$0Cd+UwAAAABJRU5ErkJggg==$

$Qn7yV4rhNLwAAAABJRU5ErkJggg==$

= 1- 0.3770 = 0.623

Therefore number measurement greater than 33.0 mm is (0.623*100= 62.3), since these are number of readings so, which is approximately 62.

In other word we can say that there 62% of measurements are greater than 33.0 mm.

The above result presented in the following table.

No. measurements of Thickness of aluminum bar less than 33.0 mm	No. measurements of Thickness of aluminum bar greater than 33.0 mm
38	62