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The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test...

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 μ = 313 and standard deviation σ = 33 .


Choose one 12th-grader at random. What is the probability (±±0.1, that is round to one decimal place) that his or her score is higher than 313 ?  Higher than 412 (±±0.0001; that is round to 4 decimal places)?


Now choose an SRS of 16 twelfth-graders and calculate their mean score x⎯⎯⎯x¯. If you did this many times, what would be the mean of all the x⎯⎯⎯x¯-values?


What would be the standard deviation (±±0.1; that is round to one decimal place) of all the x⎯⎯⎯x¯-values?


What is the probability that the mean score for your SRS is higher
than 313 ? (±±0.1; that is round to 1 decimal place)  Higher than 412 ? (±±0.0001; that is round to 4 decimal places)

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