The resistance of one meter of copper cable at a certain tem

The resistance of one meter of copper cable at a certain temperature is normally distributed with mean mu = 23.8 and variance sigma^2 = 1.28. What is the probability that a one-meter segment of copper cable has a resistance less than 23.0? What is the probability that a one-meter segment of copper cable has a resistance greater than 24.0? What is the probability that a one-meter segment of copper cable has a resistance between 24.2 and 24.5?

Solution

Solution :

Population is N ( = 23.8, ² = 1.28)

Here = 1.13

( a )

     P(Z < (23 - 23.8)/1.13 ) = P(Z < - 0.71 ) = P(Z < - 0.71) = 0.2389 from the z-table

Hence, the probability that a one-meter segment of copper cable has a resistance less than 23.0 is 0.2389 .

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( b )

  P(Z > (24 - 23.8)/1.28 ) = P(Z > 0.17699 ) = 1 - P(Z < 0.18 ) =1 - 0.5714 = 0.4286 from the z-table

  Hence, the probability that a one-meter segment of copper cable has a resistance greater than 24.0 is 0.4286 .

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( c )

P(24.2 - 23.8)/1.13 < Z < (24.5 - 23.8)/1.13 ) = P(0.35 < Z < 0.62 ) = P(Z < 0.62 ) - P(Z < 0.35 )

= 0.7324 - 0.6368 = 0.0956 from the z-table

Hence, the probability that a one-meter segment of copper cable has a resistancebetween 24.2 and 24.5 is 0.0956