# Reliability using normal distribution

Assume you tested svereral Firestone tires and recorded their failure times (as defined by an engineer).After doing a Chi-Square test ,you decided taht failures are normally distributed ,with mean failure of 50,000 miles and a standard deviation of 10,000 miles .Determine the following:

a) reliability of the tires at 40,000 miles

b) given that a tire has been driven (on a test machine) 20,000 miles, determine its reliability at 60,000 miles.

https://brainmass.com/economics/applied-economics/reliability-using-normal-distribution-71730

#### Solution Preview

Mean=M = 50,000 miles

Standard deviation =s= 10,000 miles

x= 40,000 miles

z=(x-M )/s= -1 =(40000-50000)/10000

Cumulative Probability corresponding to z= -1 is= 0.1587

Or Probability corresponding to x< 40,000 is ...

#### Solution Summary

Reliability has been calculated using normal distribution.

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