Consider again the company making tires for bikes is concerned about the exact width of their...

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.

	(Round your answer to 4 decimal places.)
a.	What is the probability that a tire will be too narrow?

	(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?

Solutions

Expert Solution

The following question can be solved in Excel using the norm.dist function.

1) Cumulative probabilities

2) Formulas used

Frome the above images, we can see that the cumulative probability of tire being up to 23 mm is 0.2023 and the cumulative probability of tire being up to 23.2 mm is 0.7977

Ans a)

The probability that a tire will be too narrow is the probability of the tire being less than 23mm. Hence, in this case, the probability of the tire being less than 23mm will be equal to the cumulative probability of tire being up to 23 mm,i.e. 0.2023

Ans b)

The probability that a tire will be too wide is the probability of the tire being more than 23.2 mm. Hence, in this case, the probability of the tire being more than 23.2 mm will be

= (1 - cumulative probability of tire being up to 23.2 mm)

= (1 - 0.7977)

= 0.2023

Ans c)

The probability that the tire will be defective is the sum total of the probability that a tire will be too narrow and the probability that a tire will be too wide.

= 0.2023 + 0.2023

= 0.4046

keosha answered 1 week ago

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