Question

A cutting tool wears out with a time to failure that is normally distributed with a mean of 10 working days and a standard deviation of 2.5 days. (a) determine its design life for a reliability of 0.99. (b) find the reliability if the tool is replaced every day; every two days; every five days. (c) determine the probability that the cutting tool will last one more day given it has been in use for 5 days.

Answer 1

Using the normalized distribution it is possible to calculate the value of Z score and for cases where there is a 99% chance, so Zscore is -3.6 and X= 16.45.

What are the types of probability distribution?

This curve determines the probability of the event associated with it occurring. The Gaussian distribution is the most common, hence it is known as the Normal Distribution. The area under the distribution curve is always equal to 1.0.

The formula for this distribution can be described as:

$Z score = \frac{x-\mu}{\sigma}$

Where:

• x= Probability density function
• μ= Mean
• σ= Standard Deviation

In this case,

$Z score =\frac{1-10}{2.5} \\Z score = -3.6$

P-value from Z-Table will be P(x<1) = 0.00015911

For 99% we have that z will be 2.58, so

$2.58=\frac{x-10}{2.5}\\x = 16.45$

See more about normally distributed at brainly.com/question/15103234

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