Submit a single PDF containing all your answers. You may write answers by hand, scan them/take a photo, and include the image. 1. A powerlifter is preparing for a competition and is wondering which of her lifts she should focus on. Her current personal bests are 127.5kg squat, 97.0kg bench press, and 150.0 kg deadlift. The mean and standard deviation of previous competitors in her weight class are given below. The results from each lift are nearly normally distributed. Mean (kg) SD (kg) Squat 111.7 28.1 Bench 66.2 19.6 Deadlift 136.0 29.1 a. Calculate the Z-scores for each of her lifts. Which lift is the weakest? Why? [/4] b. What percent of previous competitors deadlift less than her? Include a sketch of the distribution with the area of interest. [/3] C. The athlete wants to be in the top 2% of bench pressers for her category. How much will she need to bench press to achieve this? Include a sketch of the distribution with the area of interest. [/3] d. How would your answers change if the data from previous competitions were not normally distributed? [/1] 2. A recent survey by the Agri-Food Analytics Lab at Dalhousie University found that 29.3% of Canadians buy enough fruits and vegetables to meet the daily recommendations of the Canada Food Guide. A researcher in Ottawa believes that the diet of people in Ottawa differs from this. He surveys a random sample of 187 people in Ottawa and finds that 77 of them buy enough fruits and vegetables to meet the daily recommendations of the Canada Food Guide. a. Follow the Prepare, Check, Calculate, and Conclude steps to construct the 98% confidence interval for the fraction of people in Ottawa who buy enough fruits and vegetables to meet recommended amount and interpret it in context. [/7] b. Write the null and alternative hypotheses for the researcher's question. [/1] c. Use the confidence interval you calculated in a) to check if the researcher's belief is true at a significance level of 0.02 (i.e., using the 98% confidence interval). [/2] 3. In the 2021 Canadian election, 33.7% of voters voted for candidates from the Conservative Party of Canada. A poll by Nanos/CTV-Globe & Mail conducted the day before the election surveyed a random sample of 832 eligible voters and found that 31% were planning to vote Conservative. Conduct a hypothesis test using the Z-score to check whether the poll results were significantly different than the election outcome at a significance level of 0.05. Follow the Prepare, Check, Calculate, and Conclude steps. [/9]