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# Probability Distribution (4).docx

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School
Department
Statistics
Course
STATS 2B03
Professor
Aaron Childs
Semester
Fall

Description
September 28 , 2012 Stats 2B03: Statistical Methods for Science Probability Distribution (4) 4.7 The Normal Distribution - Result: If x is a normal r.v. with mean μ and variance σ then the area under the normal curve between a and b is the same as the area under the standard normal curve between - Example: the length of human pregnancies are normally distributed with mean 268 days and standard deviation 15 days b) what percentage of pregnancies last longer than 300 days? P(x>300) = 1 - .9834 .0166 =1.66% c) only 10% of pregnancies last less than ? days P(x)=.10 .1=.9 -268=-(15)(1.28) 8 - Example: suppose that marks on a test are normally distributed with μ=75. Find σ if 15% of the class got over 90 P(x>90)=.15 σ=14.423 4.7.2 Determining Normality (pp.46-49 in the courseware) - Given a population of values we can draw a histogram to see if the population follows a normal distribution - Given a sample of values, how do we determine if the population follows a normal distribution  Notation: Let Zαbe the value Z with the property that the area unse the standard normal curve
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