# Lesson 5, The gaussian (Normal) Distribution

### Lesson 5

### The Gaussian (Normal) Distribution

Consider the following scenario and answer the following 4 two-part questions.

The life of Sunshine CD players is normally distributed with a mean of 4.7 years and a standard deviation of 1.2 years. A CD player is guaranteed for 3 years.

1. We are interested in the length of time a CD player lasts.

a. Find the probability that a CD player will break down during the guarantee period. P(0<x<____) = _______

b. Sketch and shade a normal curve to indicate the probability we are interested in. Be sure to label and scale the horizontal axis.

2. Some CD players last up to 6 years.

a. Find the probability that a CD player will last between 2.75 and 6 years.

b. Sketch and shade a normal curve as in question 1.b.

3. An executive wants to know the 90^{th} percentile for CD player life.

a. Find the 90^{th} percentile for the length of time a CD player lasts.

b. Sketch and shade a normal curve as in question 1.b.

4. The engineers want to know what is typical for these CD players.

a. Find the lower and upper bounds for CD player life for the middle 85% of CD players produced

b. Sketch and shade a normal curve as in question 1.b.**Grading:** *each part ‘a” is worth 15 points, each part ‘b’ is worth 10 points*