The fracture strength of a certain type of manufactured glas

The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 509 MPa with a standard deviation of 17 MPa.

What is the probability that a randomly chosen sample of glass will break at less than 509 MPa? (Round your answer to 2 decimal places.)

What is the probability that a randomly chosen sample of glass will break at more than 528 Mpa? (Round your answer to 4 decimal places.)

What is the probability that a randomly chosen sample of glass will break at less than 535 MPa? (Round your answer to 4 decimal places.)

Solution

(a) P(X<509) = P((X-mean)/s <(509-509)/17)

=P(Z<0) = 0.5(from standard normal table)

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(b) P(X>528) = P(Z>(528-509)/17)

=P(Z>1.12) =0.1314 (from standard normal table)

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(c) P(X<535) = P(Z<(535-509)/17)

=P(Z<1.53) =0.9370 (from standard normal table)