The length of injection-molded plastic case which holds magnetic tape is normally distributed with the length of 90.2 millimeters and standard deviation of 0.1 millimeter.
a. Determine the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters?
b. What should the process mean be set at to obtain greatest number of parts between 89.7 and 90.3 millimeters?
c. If parts that aren't between 89.7 and 90.3 millimeters are scrapped, what is the yield (proportion of usable parts) for process mean that you selected in part (b)?
Suppose that the process is centered so that mean is 90 millimeters and the standard deviation is 0.1 millimeter. Assume that 10 cases are measured, and they are supposed to be independent.
d. Determine the probability that all 10 cases are between 89.7 and 90.3 millimeters.
e. Determine the expected number of the 10 cases that are between 89.7 and 90.3 millimeters?