The article “A Music Key Detection Method Based on Pitch Class Distribution Theory” (J. Sun, H. Li, and L. Ma, International Journal of Knowledge-based and Intelligent Engineering Systems, 2011:165–175) describes a method of analyzing digital music files to determine the key in which the music is written. In a sample of 335 classical music selections, the key was identified correctly in 293 of them.

a. Find a 90% confidence interval for the proportion of pieces for which the key will be correctly identified.

b. How many music pieces should be sampled to specify the proportion to within ± 0.025 with 90% confidence?

c. Another method of key detection is to be tested. At this point, there is no estimate of the proportion of the time this method will be identified correctly. Find a conservative estimate of the sample size needed so that the proportion will be specified to within ± 0.03 with 90% confidence.