In a test of Murphy’s law, pieces of toast were buttered on one side and then dropped. Mur- phy’s law predicts that they will land butter-side down. Out of 9821 slices of toast dropped, 6101 landed butter-side down. (Believe it or not, these are real data!10) a. What is a 95% confidence interval for the probability of a piece of toast landing butter- side down? b. Using the results of part (a), is it plausible that there is a 50:50 chance of the toast land- ing butter-side down or butter-side up?

Answer:a) =(0.6116259, 0.6308137) (b) No, because the interval does not include 0.5Step-by-step explanation:Given Data:sample size, n = 9821Sample, x = 6101(a) sample proportion [tex]p = \frac{6101}{9821} = 0.6212198[/tex]Given a=0.05, so Z(0.025) = 1.96 [via. standard normal table)So 95% confidence interval is[tex]p \pm Z\times \sqrt{(p\times \frac{(1-p)}{n})}[/tex][tex]=  0.6212198 \pm 1.96\times \sqrt{(0.6212198\times \frac{(1-0.6212198)}{9821})[/tex]=(0.6116259, 0.6308137)(b) No, because the interval does not include 0.5