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1. F & G industries manufacturers a motor that is marketed with a warranty that guarantees it will be replaces free of charge if it fails within the first 13,000 hours of operation. On average, F & G, motors operate for 15,000 hours with a standard deviation of 1,250 hours before failing. The number of operating hours before failure is approximately normally distributed. a. What is the probability that a motor will have to be replaced free of charge

User Paul Dubs
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1 Answer

5 votes

Answer:

The value is
P(X < 13000) =0.054799

Explanation:

From the question we are told that

The number of hours considered is
x= 13000 \ hours

The population mean is
\mu = 15000\ hours

The standard deviation is
\sigma = 1250\ hours

Generally the the probability that a motor will have to be replaced free of charge is mathematically represented as


P(X < 13000) = P(( X - \mu )/(\sigma ) < (13000 - 15000)/(1250) )


(X -\mu)/(\sigma ) &nbsp;= &nbsp;Z (The &nbsp;\ standardized \ &nbsp;value\ &nbsp;of &nbsp;\ X )


P(X < 13000) = P(Z<-1.6 )

From the z table the probability of (Z<-1.6 ) is


P(Z<-1.6 ) = 0.054799

So


P(X < 13000) =0.054799

User Kazenorin
by
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