How to solve this problem?

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Mathematics

Description

A company manufactures automobile transmissions. It has been determined that the lifetime (time until failure) of this transmission is normally distributed with an average of 78,000 miles and a standard deviation of 15,000 miles. What percentage of these transmissions will last at least 90,000 miles?

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Explanation & Answer

z = (90-78)/15

z = 12/15 = 4/5

P(X≥90,000)=1-P(X<90,000) 

1-P(z<0.8)=1-0.7881=0.2119, or 21% :)

Tabulated values taken from a Z-chart.


Anonymous
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