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.

1. What is the probability an individual student likes more than 10 songs from Eminem?

2. What is the probability an individual student likes less than 5.5 songs from Eminem?

Answer 1

P(X > 10) = 0.0228

P(X< 5.5) = 0.1587

Explanation:

Given that:

Mean = 7.0

standard deviation = 1.5

To find:

a) P(X>10)

Using the standard normal variation

`Z = (x -\mu)/(\sigma)`

`Z = (10 -7.0)/(1.5)`

Z =2.0

So;

P(X > 10) = P(Z > 2.0)

P(X > 10) = 1 - P(Z < 2.0)

From the tables

P(X > 10) = 1 - 0.9772

P(X > 10) = 0.0228

b) To find:

P(X < 5.5)

`Z = (x -\mu)/(\sigma)`

`Z = (5.5 - 7.0)/(1.5)`

Z = -1.0

However;

P(X< 5.5) = P(Z < -1.0)

P(X< 5.5) = 0.1587