Question

The number of songs enjoyed from Eminem by all Learn4Life students is normally distributed with a mean of 7.0 songs and a standard deviation of 1.5 songs.

What is the probability an individual student likes between 5.5 and 8.5 songs from Eminen?​

Answer 1

≈84,13%

Explanation:

To find the probability of a student liking between 5.5 and 8.5 songs from Eminem, we need to find the standard normal deviate (z-score) for each of these values and then use a standard normal table to find the area between these z-scores.

For 5.5 songs:

z = (5.5 - 7.0) / 1.5 = -1.0

For 8.5 songs:

z = (8.5 - 7.0) / 1.5 = 1.0

The area between -1.0 and 1.0 on a standard normal distribution table is approximately 0.8413. This means that the probability of an individual student liking between 5.5 and 8.5 songs from Eminem is approximately 84.13%.