1. Based on past data, the owner of a store believes that 0.43 of customers who walk in the store will make a purchase. Say, a random sample of 87 customers walk in the store and 0.54 of these made a purchase. What is the population mean of the sampling distribution of the sample proportion of customers who walk in this store and make a purchase?
2. A researcher wanted to estimate the population proportion of voters who are disappointed in the Federal government's handling of COVID-19. The researcher took a random sample of 141 voters and found 86 of these were disappointed in the Federal government. If using a 95% confidence interval, what is the value of the margin of error, to estimate the proportion of voters in Australia who are disappointed in the Federal government's handling of COVID-19. Assume all required conditions are met. Give your answer correctly rounded to two decimal places. Do NOT give your answers in percentage form.
3. You are told that a normally distributed random variable has a standard deviation of 3.33 and 97.5% of the values are above 14. What is the value of the mean? Please give your answer to two decimal places.