Question

To measure the success of the latest treatment for iPod-related deafness among young adults, researchers measured the sound sensitivity of 100 young adults by having them stand 20 feet away from a speaker playing "Slim Whitman Favorite Hits." It was found that 35% of the sample could not repeat any song lyrics from the CD. What is the variance of this distribution? o A (20)(.35) o B (20)(.65) o C (20)6.35)(.65) O D (-35)(65) o E (100)(-35) 0 F (100)(.65) o G (100)(-35)(.65) o insufficient information

Answer 1

BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is executed
p = success probability
mean = 100 * 0.35
= 35
II.
variance = npq
where
n = total number of repetitions experiment is executed
p = success probability
q = failure probability
variance = 100 * 0.35 * 0.65
= 22.75
III.
standard deviation = sqrt( variance ) = sqrt(22.75)
=4.7697
Answer:
option:G
variance of this distribution = 100*0.35*0.65 = 22.75