A supplier contract calls for a key dimension of a part to be between 1.88 and 2.12 cm. That is, a part will not be accepted if the dimension of a part is out of the specified limits. The supplier has determined that the standard deviation of its production process is 0.05 cm. The process is normally distributed. Each of the following questions is independent except question e which uses the standard deviation from question d.

If the mean is 1.95 cm, what percentage of parts will meet the specification?

If the mean is adjusted to 2.00 cm, what percentage of parts will meet the

specification?

If the mean is adjusted to 2.00 cm, the middle 95% of the parts produced will

have dimension within what limits? (Compute lower and upper limits.)

If the mean is adjusted to 2.00 cm, how small must the standard deviation be to

satisfy the six-sigma requirement? (Take 3 decimal places.)

Using the standard deviation in question d, what is the probability that a part will be out of the specified limits (smaller than 1.88 or larger than 2.12) when the mean shifts up by one standard deviation? (The new mean will be 2.00 cm + 1 standard deviation. Use Excel function to obtain probabilities.)