# Connexions

You are here: Home » Content » Collaborative Statistics » Practice: The Normal Distribution

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### In these lenses

• Exercises

This module is included inLens: Mihai Nica's Lens
By: Mihai Nica

Click the "Exercises" link to see all content selected in this lens.

• BUS204 Homework

This module is included inLens: Saylor BUS 204 Homework
By: David Bourgeois

"Normal distribution review"

Click the "BUS204 Homework" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Inside Collection (Textbook):

Textbook by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

# Practice: The Normal Distribution

## Student Learning Outcomes

• The student will analyze data following a normal distribution.

## Given

The life of Sunshine CD players is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for 3 years. We are interested in the length of time a CD player lasts.

## Normal Distribution

### Exercise 1

Define the Random Variable X X size 12{X} {} in words. X = X = size 12{X={}} {}

X X~

### Exercise 3

Find the probability that a CD player will break down during the guarantee period.

• a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.
• b. P ( 0 < x < _________ ) = _________ P ( 0 < x < _________ ) = _________ size 12{P $$0<x<"_________"$$ ="_________"} {} (Use zero (0) for the minimum value of x.)

#### Solution

• b. 3,0 . 1979 3,0 . 1979 size 12{3,0 "." "1979"} {}

### Exercise 4

Find the probability that a CD player will last between 2.8 and 6 years.

• a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.
• b. P ( _______ < x < _______ ) = _________ P ( _______ < x < _______ ) = _________ size 12{P $$"_______"<X<"_______"$$ ="_________"} {}

#### Solution

• b. 2 . 8,6,0 . 7694 2 . 8,6,0 . 7694 size 12{2 "." 8,6,0 "." "7694"} {}

### Exercise 5

Find the 70th percentile of the distribution for the time a CD player lasts.

• a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the lower 70%.
• b. P(x<k)=_________P(x<k)=_________ size 12{P $$x<k$$ ="_________"} {}. Therefore, k=__________k=__________ size 12{k="__________"} {}.

#### Solution

• b. 0.70,4.780.70,4.78 size 12{0 "." "70",4 "." "78"} {}years

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

#### Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

#### Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks