how do you solve

A musician is writing a new song and wanis to know at which tempo he should write it to break onto the pop music charts. He takes a random sample of 100 pop songs and nds an average tempo of 104 bpm with a standard deviation of 14. Where applicable, use 3 decimals in the following answers. Please carry your intermediate calculations out to 4 decimal places. a) Find the upper limit for a 95% condence interval for the average beats per minute of a pop song. b) what does the 95% condence mean? 95% of the sampled tempos will fall within this interval. 0 95% of intervals produced using this method will contain the true average beats per minute. 0 95% of the results from the sample will be valid for estimating the true average beats per minute. 0 95% of samples will produce an interval containing this sample average number of beats per minutes. c) A producer asks the musician to produce a new interval. In particular, he wants the estimate to be within 1.32 bpm of the true average with 95% condence. Assuming the standard deviation remains unchanged, how many songs would the musician need to sample? E Marketing contends that celebrity endorsements of products spur sales of that product. A study from 2013 gathered a random sample of 1200 commercials and found that 15% of them featured a celebrity. They created a confidence interval to estimate the proportion of all commercials that feature a celebrity to within 2.7%. a) Based on this confidence interval, which of the following must be true? O Approximately 2.7% of all commercials were sampled. O With 97.3% confidence, 15% of all commercials feature a celebrity. It is reasonable to conclude that 18.5% of all commercials feature a celebrity. O It is reasonable to conclude that 13% of all commercials feature a celebrity. O Between 12.3% and 17.7% of all celebrities have been featured in commercials. b) Suppose the researchers wanted to increase the width of the confidence interval. What could they do? the sample size. Alternatively, - the confidence level