Question

Ayla has liked thousands of songs on Spotify. The distribution of play times for these songs has a mean of 175 seconds and a standard deviation of 55 seconds. If 36 of Ayla’s “liked” songs are randomly sampled, what is the probability that the average length of these 36 songs is less than 185 seconds?

Answer 1

µ =    175                  
σ =    55                  
n=   36                  
                      
X =   185                  
Z =(X - µ )/(σ/√n) =    (185-175)/(55/√36)=               1.09  
P(X ≤   185   ) = P(Z ≤   1.09   ) =   0.8623   (answer)