Question

-ch7. The number of songs enjoyed from Dr. Dre by Learn4Life students schoolwide is normally distributed with amean of 8.0 songs and a standard deviation of 2.0 songs.What is the probability an individual student likes more than 10 songs from Dr. Dre?What is the probability an individual student likes between 4 and 12 songs from Dr. Dre?

Answer 1

The probability that an individual student likes more than 10 songs from Dr. Dre is 16%.

The probability that an individual student likes between 4 and 12 songs from Dr. Dre is 95%.

How to calculate the probability?

The probability that an individual student likes more than 10 songs from Dr. Dre is calculated by applying the following formula as shown below;

Mean = 8

Standard deviation = 2

One standard deviation above the mean = 8 + 2

One standard deviation above the mean = 10

From the curve, P(more than 10) = 13.5% + 2.35% + 0.15%

= 16%

The probability that an individual student likes between 4 and 12 songs from Dr. Dre is;

Two standard deviation below the mean = 8 - 2(2) = 4

Two standard deviation above the mean = 8 + 2(2) = 12

P ( between 4 and 12) = 13.5% + 34% + 34% + 13.5% = 95%

Answer 2

Since the standard deviation is 2 songs, then, a student that likes more than 10 songs falls more than 1 standard deviation from the mean of 8 songs.

The region that corresponds to that situation is highlighted in the following diagram:

Add the percentages of that region to find the answer:

`13.5+2.35+0.15=16`

Therefore, the probability that an individual student likes more than 10 songs is 16%.

4 songs is 2 standard deviations less than the mean of 8 songs, and 12 songs is 2 standard deviations more than the mean of 8 songs. The region that corresponds to that situation is highlighted in the following diagram:

Add the percentages of that region to find the answer:

`13.5+34+34+13.5=95`

Therefore, the probability that an individual student likes between 4 and 12 songs is 95%.