Consider again the company making tires for bikes is concerned about the exact w
ID: 358826 • Letter: C
Question
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 22.5 mm and an upper specification limit of 23.1 mm. The standard deviation is 0.2 mm and the mean is 22.8 mm. (Round your answer to 4 decimal places.) Round your answer to 4 decimal places.) b. What is the probability that a tire will be too wide? Round your answer to 3 decimal places.) c. What is the probability that a tire will be defective?Explanation / Answer
Given are :
Process mean = m = 22.8 mm
Process standard deviation = Sd = 0.2 mm
Upper Specification Limit = USL = 23.1 mm
Lower Specification Limit = LSL = 22.5 mm
Answer to question a :
Probability that a tyre will be too narrow = Probability that process outcome will be max equal to LSL
Let corresponding Z value for the said probability = Z1
Therefore ,
M + Z1 x Sd = LSL
Or, 22.8 + 0.2.Z1 = 22.5
Or, 0.2 .Z1 = - 0.3
Or, Z1 = - 0.3 / 0.2 = - 1.5
Corresponding probability for Z1 = - 1.5 as derived from standard normal distribution table = 0.0668
PROBABILITY THAT A TYRE WILL BE TOO NARROW = 0.0668
Answer to question b :
Probability that a tyre will be too wide will be same as probability that the process outcome will be more than USL.
Let the Z value for the probability that the process outcome will be maximum USL = Z2
Therefore ,
M + Z2x Sd = USL
Or, 22.8 + 0.2.Z2 = 23.1
Or, Z2 = 0.3/0.2 = 1.5
Corresponding value of probability for Z2 = 1.5 as derived from Standard normal distribution table will be 0.93319
Hence, probability that process outcome will be maximum USL = 0.93319
Therefore ,
Probability that a tire will be too wide
= 1 – Probability that a tire will be max USL ( i.e. 23.1 mm)
= 1 – 0.93319
= 0.0668
PROBABILITY THAT A TIRE WILL BE TOO WIDE = 0.0668
Answer to question c :
Probability that a tire will be defective
= Probability that a tire will be too narrow + probability that a tire will be too wide
= 0.0668 + 0.668
= 0.1336
PROBABILITY THAT A TYRE WILL BE TOO NARROW = 0.0668