Consider again the company making tires for bikes is concerned about the exact width of their cyclocross tires. The company has a lower specification limit of 23 mm and an upper specification limit of 23.2 mm. The standard deviation is 0.12 mm and the mean is 23.1 mm.
a. What is the probability that a tire will be too narrow? not attempted (Round your answer to 4 decimal places.)
b. What is the probability that a tire will be too wide?(Round your answer to 4 decimal places.)
c. What is the probability that a tire will be defective? (Round your answer to 3 decimal places.)
We need to calculate the z value and determine the corresponding probability from the normal distribution table.
a. Too narrow
z = (23-23.1)/0.12 = -0.833
P(z) = 0.2023
There is a probability of 0.2023 that the tire will be below specification (too narrow).
b. Too wide
z = (23.2-23.1)/0.12 = 0.833
P(z) = 0.7976
Probability will be the inverse of this value since it is on the right side of the curve. Thus 1-0.7976 = 0.2023
There is a probability of 0.2023 that the tire will be above specification.
c. Defective
Considering that the the probability of falling above and below the spec and add them up. The probability of being defective is 0.2023*2 = 0.4046
There is a 0.404 porbability that it will be defective
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