1. 15 48 S-AQ The scores of 12th-grade students on the National Assessment of Ed
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Question
1. 15 48 S-AQ The scores of 12th-grade students on the National Assessment of Educational progress year 2000 mathematics test have a distribution that is approximately Normal Choose one 12th-grader at random, what is the probability (±0.1) that his or her score is higher than 312 ? Higher than 4200.001)? Now choose an 5R5 of 16 twelfth-graders and calculate their mean score . If you did this many times, what would be the mean of all the -values? What would be the standard deviation (±0.1) of all the z values? ! th mean -312 and standa de at on 3 What is the probability that the mean score for your SRS is hi than 312 ? (±0.1) Higher than 420 ? (±0.0001)Explanation / Answer
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 312
standard Deviation ( sd )= 36
a.
P(X > 312) = (312-312)/36
= 0/36 = 0
= P ( Z >0) From Standard Normal Table
= 0.5
P(X > 420) = (420-312)/36
= 108/36 = 3
= P ( Z >3) From Standard Normal Table
= 0.0013
b.
mean of the sampling distribution ( x ) = 312
standard Deviation ( sd )= 36/ Sqrt ( 16 ) =9
sample size (n) = 16
c.
P(X > 312) = (312-312)/36/ Sqrt ( 16 )
= 0/9= 0
= P ( Z >0) From Standard Normal Table
= 0.5
P(X > 420) = (420-312)/36/ Sqrt ( 16 )
= 108/9= 12
= P ( Z >12) From Standard Normal Table
= 0
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