9 Extended: Simultaneous Equations Part 1

Complete the following questions before our next class.

Exercise 16A.1 question 2b
Exercise 16A.2 questions 1b, 2a
Exercise 16B questions 1def, 2abc (these are similar to what we did in class—substitute in one equation to get one equation with a single variable, solve for that variable, then use one of the original equations to solve for the remaining variable)
Exercise 16C questions 1abc, 2def, 3

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?