<< Chapter < Page Chapter >> Page >

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 X size 12{X} {} be the random variable representing the time it takes her to complete one review. Assume X size 12{X} {} is normally distributed. Let X ¯ size 12{ {overline {X}} } {} be the random variable representing the mean time to complete the 16 reviews. Let ΣX 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. X ~
  2. X ~
  3. ΣX ~

Graphing probability

For each problem below:

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

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

  • Empty normal distribution curve graph with x-axis of x.
  • P ( size 12{P \( } {} ________ < x < size 12{<x<} {} ________ ) = size 12{ \) ={}} {} _______

  • 3.5, 4.25, 0.2441

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

  • Empty normal distribution curve graph for the average.
  • P (________________ ) = _______

  • 0.7499

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

  • Empty normal distribution curve graph for Sum X.
  • The Probability=

  • 0.3802

Discussion question

What causes the probabilities in [link] and [link] to differ?

Questions & Answers

what are components of cells
ofosola Reply
twugzfisfjxxkvdsifgfuy7 it
Sami
58214993
Sami
what is a salt
John
the difference between male and female reproduction
John
what is computed
IBRAHIM Reply
what is biology
IBRAHIM
what is the full meaning of biology
IBRAHIM
what is biology
Jeneba
what is cell
Kuot
425844168
Sami
what is cytoplasm
Emmanuel Reply
structure of an animal cell
Arrey Reply
what happens when the eustachian tube is blocked
Puseletso Reply
what's atoms
Achol Reply
discuss how the following factors such as predation risk, competition and habitat structure influence animal's foraging behavior in essay form
Burnet Reply
cell?
Kuot
location of cervical vertebra
KENNEDY Reply
What are acid
Sheriff Reply
define biology infour way
Happiness Reply
What are types of cell
Nansoh Reply
how can I get this book
Gatyin Reply
what is lump
Chineye Reply
what is cell
Maluak Reply
what is biology
Maluak
what is vertibrate
Jeneba
what's cornea?
Majak Reply
what are cell
Achol
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics using spreadsheets' conversation and receive update notifications?

Ask