Connexions

You are here: Home » Content » Collaborative Statistics » Practice: The Central Limit Theorem

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

• Lucy Van Pelt

This collection is included inLens: Lucy's Lens
By: Tahiya Marome

"Part of the Books featured on Community College Open Textbook Project"

Click the "Lucy Van Pelt" link to see all content selected in this lens.

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

• 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.

• Bio 502 at CSUDH

This collection is included inLens: Bio 502
By: Terrence McGlynn

"This is the course textbook for Biology 502 at CSU Dominguez Hills"

Click the "Bio 502 at CSUDH" 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 Central Limit Theorem

Student Learning Outcomes

• The student will calculate probabilities using 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 mean 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. Assume that the 16 reviews represent a random set of reviews.

Distribution

Complete the distributions.

1. XX ~
2. X¯X ~
3. ΣXΣX ~

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 mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.

• a.
• b. P(________________ )=P(________________ )=_______

• b. 0.7499

Exercise 3

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

• a.
• b. The 95th Percentile=

Solution

• b. 4.49 hours

Exercise 4

Find the probability that the sum of the month’s reviews takes Yoonie from 60 to 65 hours.

• a.
• b. The Probability=

• b. 0.3802

Exercise 5

Find the 95th percentile for the sum of the month’s reviews.

• a.
• b. The 95th percentile=

• b: 71.90

Discussion Question

Exercise 6

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.

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