S-AQ) The scores of 12th-grade students on the National Assessment of Educationa

Question

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 = 273 and standard deviation = 34.

Choose one 12th-grader at random. What is the probability (±0.1) that his or her score is higher than 273?            Higher than 341 (±0.001)?    

Now choose an SRS of 4 twelfth-graders and calculate their mean score x¯. If you did this many times, what would be the mean of all the x¯-values?    

What would be the standard deviation (±0.1) of all the x¯-values?    

What is the probability that the mean score for your SRS is higher
than 273? (±0.1)      Higher than 341? (±0.0001)     

Explanation / Answer

z=(273-273)/34

z=0

P(z>273)=0.5±0.1

z=(341-273)/34

z=2

P(z>2)=0.023±0.001

Now choose an SRS of 4 twelfth-graders and calculate their mean score x¯. If you did this many times, what would be the mean of all the x¯-values?    
The Central Limit Theorem would like miu 273

What would be the standard deviation (±0.1) of all the x¯-values?    

he Central Limit Theorem would like sigma 34

What is the probability that the mean score for your SRS is higher
than 273? (±0.1)      Higher than 341? (±0.0001)   

z=(273-273)/(34/sqrt(4)

z=0

P(z>273)=0.5±0.1

z=(341-273)/(34/sqrt(4)

z=4

P(z>273)=0.000032

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