Question

Pandora Radio has determined that the probability of a user liking a new song enough to give a "thumbs up" is 0.7509. Given that Pandora plays about 511 new songs per user per month on average, what is the probability that between 372 and 393 (inclusively) of those plays get a "thumbs up"?

Question 14 options:

1)

0.7350

2)

0.0461

3)

0.0091

4)

0.9680

5)

0.2650

Answer 1

Mean = n * P = ( 511 * 0.7509 ) = 383.7099
Variance = n * P * Q = ( 511 * 0.7509 * 0.2491 ) = 95.5821
Standard deviation = √(variance) = √(95.5821) = 9.7766

P ( 372 <= X <= 393 )
Using continuity correction
P ( n - 0.5 < X < n + 0.5 ) = P ( 372 - 0.5 < X < 393 + 0.5 ) = P ( 371.5 < X < 393.5 )

X ~ N ( µ = 383.7099 , σ = 9.7766 )
P ( 371.5 < X < 393.5 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 371.5 - 383.7099 ) / 9.7766
Z = -1.25
Z = ( 393.5 - 383.7099 ) / 9.7766
Z = 1
P ( -1.25 < Z < 1 )
P ( 371.5 < X < 393.5 ) = P ( Z < 1 ) - P ( Z < -1.25 )
P ( 371.5 < X < 393.5 ) = 0.8410 - 0.1060
P ( 371.5 < X < 393.5 ) = 0.7350