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BYU-I - MATH 221 - Class Notes - Week 4

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BYU-I - MATH 221 - Class Notes - Week 4

School: Brigham Young University - Idaho
Department: OTHER
Course: Business Statistics
Professor: J. Hathaway
Term: Fall 2018
Tags: Statistics
Name: Math 221A
Description: This covers week 4 lessons on sample distribution and probability.
Uploaded: 10/12/2018
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background image Review of Sampling Distributions When the sample is mean normally distributed (or approximately normally distributed)? This  happens when either of the two conditions are satisfied:  The parent population is normally distributed, so the sample mean is 
automatically normally distributed.
The sample size is large, and the Central Limit Theorem implies that the sample 
mean is normally distributed.
For the mean of draws from a random variable with mean  μ And standard deviation  σ , the following are true:  The mean of the random variable  X¯ Is  μ •   . 
•  the standard deviation of the random variable 
X¯  is  σn−−√ . Probabilities Involving a Mean If the sample mean is normally distributed, then we can consider the sample mean,  x¯ , as one observation from a normal distribution with mean  μ  and standard deviation  σn−−√ With this in mind, we can compute the  z ­Score for any value of this random variable:  z=value−mean standard deviation=x¯−μσ/n−−√ Example: Finding the Area under a Normal Curve (Based on a Sample Mean)  After finding the  z ­score, we can use the normal probability applet to find the area under the  curve (i.e. the probability.) Suppose that a sample of size  n=4  has been drawn from a normal  population with mean  μ=7  and standard deviation  σ=3 . Since the parent population is  normal, we know the sampling distribution of the sample mean  x¯  will be normal with mean 

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School: Brigham Young University - Idaho
Department: OTHER
Course: Business Statistics
Professor: J. Hathaway
Term: Fall 2018
Tags: Statistics
Name: Math 221A
Description: This covers week 4 lessons on sample distribution and probability.
Uploaded: 10/12/2018
2 Pages 40 Views 32 Unlocks
  • Better Grades Guarantee
  • 24/7 Homework help
  • Notes, Study Guides, Flashcards + More!
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