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