Question

please solve and highlight answers

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 0.0005 (a)If 34 students at Julliard School of Music are tested, and 3 are found to have perfect pitch. would you conclude at the 0.01 level of significance that Julliard students are more likely than the general population to have perfect pitch? Yes No (b) Normality should not be assumed because a. only 3 students had perfect pitch. b. the product of n and o is too small. c. all students had perfect pitch. d. no student had perfect pitch a O C O OOO

Answer 1

a)P(getting 3 or more with perfect pitch) =P(X>=3) =1-P(X<=2)

=1-(P(X=0)+P(X=1)+P(X=2))=1-((34C0)*(0.0005)⁰(0.9995)³⁴+(34C1)*(0.0005)¹(0.9995)³³+(34C2)*(0.0005)²(0.9995)³²)

=0.000001

as probability of above event is significantly smaller than 0.01 level, we reject null and conclude that Julliard students are more likely to have a perfect pitch

YEs

b)

option B (as n$\pi$0 should be at least 5 for normal approximation)