diff --git a/source/exams/exam-02.ptx b/source/exams/exam-02.ptx index 4f81cf7..2543598 100644 --- a/source/exams/exam-02.ptx +++ b/source/exams/exam-02.ptx @@ -187,7 +187,7 @@

- S is binomially distributed with E(S) = (180)(0.7) = 126 and \Var(S) = (180)(0.7)(0.3) = 37.8. Therefore: + S is binomially distributed with \E(S) = (180)(0.7) = 126 and \Var(S) = (180)(0.7)(0.3) = 37.8. Therefore: \Pr(120 \leq S \leq 130) \amp \approx \Pr\left( \frac{119.5 - 126}{\sqrt{37.8}} \leq Z \leq \frac{130.5 - 126}{\sqrt{37.8}}\right) \amp \approx \Pr(-1.06 \leq Z \leq 0.73) @@ -204,7 +204,7 @@

The weights of five apples are measured and recorded below. - Find the sample mean, sample variance, and a 95\% confidence interval around the sample mean for the weights of the apples. + Find the sample mean, sample variance, and a 95% confidence interval around the sample mean for the weights of the apples. (Pretend that 5 measurements is enough for the CLT to apply. Do not use the t-distribution.)

@@ -329,11 +329,11 @@ If the coin is fair, then \E(S) = (160)(0.5) = 80 and \Var(S) = (160)(0.5)(0.5) = 40. The probability of rejecting H_0 is then: - \Pr(S \geq 75) \amp \approx \Pr\left(Z \geq \frac{75 - 80}{\sqrt{40}}\right) - \amp \approx \Pr(Z \geq -0.79) - \amp \approx 1 - \Phi(-0.79) - \amp \approx 1 - 0.2148 - \amp = 0.7852. + \Pr(S \geq 75) \amp \approx \Pr\left(Z \geq \frac{74.5 - 80}{\sqrt{40}}\right) + \amp \approx \Pr(Z \geq -0.87) + \amp \approx 1 - \Phi(-0.87) + \amp \approx 1 - 0.1922 + \amp = 0.8078.