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11. [-/17 Points] DETAILS ILLOWSKYINTROSTAT1 8.HW.118. MY NOTES Suppose that insurance companies did a survey. They randomly surveyed 420 drivers and found that 310 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) + Part (a) Part (b) Part (c) Which distribution should you use for this problem? (Round your answer to four decimal places.) P' ~ Explain your choice. O The binomial distribution should be used because there are two outcomes, buckle up or do not buckle up. O The Student's t-distribution should be used because we do not know the standard deviation. The Student's f-distribution should be used because v npq s 10, which implies a small sample. The normal distribution should be used because we are interested in proportions and the sample size is large. Part (d) Construct a 95% confidence interval for the population proportion who claim they always buckle up. (i) State the confidence interval. (Round your answers to four decimal places.)