The scores of 12thgrade students on the National Assessment

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 = 310 and standard deviation = 32.

1) Choose one 12th-grader at random. What is the probability (±0.1) that his or her score is higher than 310? ,5 Higher than 374 (±0.001)?

2) 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?

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

4)What is the probability that the mean score for your SRS is higher than 310? (±0.1) Higher than 374? (±0.0001)

Solution

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 = 310 and standard deviation = 32.

1) Choose one 12th-grader at random. What is the probability (±0.1) that his or her score is higher than 310? ,5 Higher than 374 (±0.001)?

Z value for 310, z=(310-310)/32 =0

P( x >310) = p( z >0) =0.5

Z value for 374, z=(374-310)/32 =2

P( x >374) = p( z >2) =0.023

2) 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?

Mean value =310

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

Sd=sd/sqrt(n) = 32/srt(4) =16.0

4)What is the probability that the mean score for your SRS is higher than 310? (±0.1) Higher than 374? (±0.0001)

Z value for 310, z=(310-310)/16 =0

P( mean x >310) = p( z >0) =0.5

Z value for 374, z=(374-310)/16 =4

P( mean x >374) = p( z >4) =0.0000