12 HL The Normal Distribution

Here’s the question we were looking at in class, complete this question (and the other questions that I’ll include in an email to you) before our next class.

An manufacturing process produces aircraft parts such that the length of each part, X, (in cm) is such that \(X\sim N(\mu,\sigma^2)\).

We know that \(P(X\leq 120)=0.4596\) and \(P(X\leq 132)=0.6491\).

Find \(\mu\) and \(\sigma\).

If a part is rejected if it is more than 1 cm away from the mean, what percentage of parts are rejected?

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