# Connexions

You are here: Home » Content » Collaborative Statistics: Custom Version modified by V Moyle » Practice: Central Limit Theorem (modified R. Bloom)

### Recently Viewed

This feature requires Javascript to be enabled.

Inside Collection (Textbook):

Textbook by: Vicky Moyle. E-mail the author

# Practice: Central Limit Theorem (modified R. Bloom)

Module by: Roberta Bloom. E-mail the authorEdited By: Roberta Bloom

Summary: This module contains practice problems for the Central Limit Theorem from Collaborative Statistics by Susan Dean and Dr. Barbara Illowsky. The problems relating to Central Limit Theorem for averages have not been changed in this module. The problems relating to Central Limit Theorem for sums have been removed from this module.

## Student Learning Outcomes

• The student will explore the properties of data through the Central Limit Theorem.

## Given

Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately 4 hours each to do with a population standard deviation of 1.2 hours. Let XX size 12{X} {} be the random variable representing the time it takes her to complete one review. Assume XX size 12{X} {} is normally distributed. Let X¯X¯ size 12{ {overline {X}} } {} be the random variable representing the average time to complete the 16 reviews. Let ΣXΣX size 12{ΣX} {} be the total time it takes Yoonie to complete all of the month’s reviews.

## Distribution

Complete the distributions.

1. XX ~
2. X¯X ~

## Graphing Probability

For each problem below:

• a. Sketch the graph. Label and scale the horizontal axis. Shade the region corresponding to the probability.
• b. Calculate the value.

### Exercise 1

Find the probability that one review will take Yoonie from 3.5 to 4.25 hours.

• a.
• b. P(P( size 12{P $$} {} ________ <X<<X< size 12{<X<} {} ________ )=)= size 12{$$ ={}} {} _______

#### Solution

• b. 3.5, 4.25, 0.2441

### Exercise 2

Find the probability that the average of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.

• a.
• b. P( )=P( )=_______

#### Solution

• b. 0.7499
• NOTE:. When calculating the standard deviation for the mean using the Central Limit Theorem in this problem, the sample size is n = 16, the number of reviews she completes in a month.

### Exercise 3

Find the 95th percentile for the average time to complete one month’s reviews.

• a.
• b. The 95th Percentile=

#### Solution

• b. 4.49 hours

## Discussion Question

### Exercise 4

What causes the probabilities in Exercise 1 and Exercise 2 to differ?

## 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.

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

PDF | EPUB (?)

### What is an EPUB file?

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

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

#### 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