What proportion of cases produced have a width that is less than 3.014 inches?

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A manufacturer of cell phone cases monitors the machines closely to make sure they are producing cases that do not vary far from the desired dimensions. One specific dimension of interest is the width of the case. The width of produced cases varies Normally with a mean of 2.98 inches and a standard deviation of 0.05 inches.

a) What proportion of cases produced have a width that is less than 3.014 inches?

b) What is the 25th percentile for the width of the cases produced, in inches?

c) An outlier is any value that falls at least 1.5 times the interquartile range (IQR) above Q3 or below

Q1. If the width of a case is an outlier, that case must be discarded. What proportion of all cases will be discarded?

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