1. (15.48 S-AQ) The scores of 12th-grade students on the National Assessment of
ID: 3305058 • Letter: 1
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 with mean 324 and standard deviation Choose one 12th grader at random what is the probability ±0.1 that is round to one decimal place that his or her score s h gher than 324 ? Higher than 394 ±0.0001; that s round to 4 decimal places)? Now choose an SRS of 16 twelfth-graders and calculate their mean score E. If you did this many times, what would be the mean of all the E values? what would be the standard deviation (20.1; that is round to one decimal place) of all the z-values? 35 What is the probability that the mean score for your SRS is higher than 324 ? (±0.1; that is round to 1 decimal place) Higher than 394 ? (±0.0001; that is round to 4 decimal places) Check Syntax Syntax OK Recall how the sample mean of an SRS is distributed, and that sample standard deviation is the standard deviation of the measured variable divided by the square root of the sample size.Explanation / Answer
we are givne that mean = 324 and sd = 35
P(x>324)
so we use the z score formula as
Z = (X-mean)/sd = (324-324)/35 = 0
P(z>0), please keep the z tables handy for this now
P ( Z>0 )=1P ( Z<0 )=10.5=0.5
P(x>394 )
so we use the z score formula as
Z = (X-mean)/sd = (394-324)/35 = 2
P(z>2)
P ( Z>2 )=1P ( Z<2 )=10.9772=0.0228
the mean of the sample would be 324 , if we do this many times , the mean of the sample would tend to be 324
The standard deviation of the 16 students would be
Sd/sqrt(n) = 35/sqrt(16) = 8.75
Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines. However the concept for calculation the last part remains same as that of the first part of the question
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