Perfect pitch is the ability to identify musical notes correctly without hearing another note as a reference. The probability that a randomly chosen person has perfect pitch is .0005.
(a) If 20 students at Julliard School of Music are tested, and 2 are found to have perfect pitch, would you conclude at the .01 level of significance that Julliard students are more likely than the general population to have perfect pitch? Use Excel to find the right-tailed binomial probability P(X ≥ 2 | n = 20, π = .0005). Alternatively, use MINITAB.
(b) Show that normality of the sample proportion p should not be assumed.