PS296 Lecture Notes - Lecture 5: Standard Deviation

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23 May 2018
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What is the probability of scoring 1 or more standard deviations above the mean?
-using the smaller portion, look up on the chart a z score of 1
-with a z score of 1, the probability of the smaller portion (red section) is 1.587
What is the probability of scoring between 1 and 2 standard devitions above the mean?
-for z = 2.00, probability is .4772 (mean to z)
-for z = 1.00, probability = .3413 (mean to z)
-to find the probability between 1.00 and 2.00: find the probabilty of mean to 1 and
subtract it from probability of mean to 2
.4772 - .3413 = .1359
Another way to find this:
-find the probability of a larger portion of the curve
-for z = 2.00, the larger portion is .9773 (this is the portion from -3 to 2, not just 0 to 2)
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Document Summary

Using the smaller portion, look up on the chart a z score of 1. With a z score of 1, the probability of the smaller portion (red section) is 1. 587. For z = 2. 00, probability is . 4772 (mean to z) For z = 1. 00, probability = . 3413 (mean to z) To find the probability between 1. 00 and 2. 00: find the probabilty of mean to 1 and subtract it from probability of mean to 2. Find the probability of a larger portion of the curve. For z = 2. 00, the larger portion is . 9773 (this is the portion from -3 to 2, not just 0 to 2) Now, find probability of larger portion of 1. 00 (. 8413) To find probability between 1 and 2, do . 9772 - . 8413 = . 1359. A packng machine is set to fill a cardboard box with an average of 15oz of cereal. Suppose the amounts per box form a normal distirbution with a standard deviation of .

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