To find the probability that a given voicemail is between 20 and 50 seconds, we need to find the area under the normal curve between these two values.
Using the 68-95-99.7 rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this case, we want to find the probability that a voicemail falls within one standard deviation below the mean and one standard deviation above the mean, which corresponds to the interval (30,50).
To find this probability, we can use a standard normal distribution table, or we can convert the values to z-scores and use the standard normal distribution formula.
Using the formula, we have:
z1 = (20 - 40) / 10 = -2
z2 = (50 - 40) / 10 = 1
Now we look up the probability of a standard normal distribution between -2 and 1, which is approximately 0.818.
Therefore, the probability that a given voicemail is between 20 and 50 seconds is 81.8%.
P = 81.8%.