Consider again that the company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a

lower specification limit of $22\mathrm{.}8$ millimeters and an upper specification limit of $23\mathrm{.}2$ millimeters. The standard deviation is $0\mathrm{.}15$

millimeters and the mean is $23$ millimeters.

a$.$ What is the probability that a tire will be too narrow?

Note: Round your answer to $6$ decimal places.

Probability

b$.$ What is the probability that a tire will be too wide?

Note: Round your answer to $6$ decimal places.

Probability

c$.$ What is the probability that a tire will be defective?

Note: Round your answer to $6$ decimal places.

Probability