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Question 5: RCMP detachments are concerned about traffic speeds in school zones, hence they use speedmeasuring machines on roads to measure how fast the motorists are driving. Following speed measurements (in \( \mathrm{kms} / \mathrm{h} \) ) were reported by a speed-measuring machine placed at the school-zone in New Minas: (5\%) (a) Calculate the sample size, the sample mean and the sample standard deviation for your sample. Sample size: Sample mean: Sample standard deviation: (6\%) (b) Using the information from your sample, construct a confidence interval estimate for the average speed of motorists at the school-zone in New Minas at the \( 99 \% \) level of confidence. Interpret your interval. Based on your interval estimates, do you have a reason to believe that motorists are breaking the law (i.e. travel above the legal speed limit of \( 30 \mathrm{~km} / \mathrm{h} \) )? Explain your answer. (6\%) (c) Calculate the proportion of motorists that travel beyond the legal speed limit in your sample. Construct a confidence interval estimate for the true proportion of motorists that travel beyond the legal speed limit (i.e. \( 30 \mathrm{~km} / \mathrm{h} \) ) at the school-zone in New Minas at the \( 95 \% \) level of confidence. Interpret your interval.

a) Sample size (n) = 48 Sample mean ( x?) = ?xin=1,49648=31.167 Sample standard deviation (s) = ?(xi?x?)2n?1=648.66748?1=3.715

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