The average length of a song is 3.25 minutes with a standard deviation of 0.35 minutes. Use a spreadsheet program to find the probability that a song chosen at random will be longer than 3.7 minutes.
To find the probability that a song chosen at random will be longer than 3.7 minutes, we can use the z-score formula:
z = (x - μ) / σ
Where:
x = 3.7 minutes
μ = 3.25 minutes
σ = 0.35 minutes
Plugging in the values, we get:
z = (3.7 - 3.25) / 0.35
z = 1.29
Now, we can use a z-score table or a spreadsheet program to find the probability that a z-score of 1.29 corresponds to. In this case, the probability is approximately 0.9015, or 90.15%.
Therefore, the probability that a song chosen at random will be longer than 3.7 minutes is 90.15%.