Question

According to media research, the typical american listened to 195 hours of music per year (µ=195). john trythall is a big country and western music fan. he listens to music while working around the house, reading and riding in his truck. assume the number of hours spent listening to music follows a normal distribution with a standard deviation of 8.5 hours (σ=8.5). if john is in the top 1 percent in terms of listening time, at least how many hours does he listen per year?

Answer 1

From a standard normal distribution table, the z-score corresponding to a cumulative probability of 0.99 is 2.33:
$2.33=\frac{X-195}{8.5}$
$X=2.33\times8.5+195=214.8$
The answer is: John listens at least 214.8 hours per year.