SOLUTION: A distribution of scores has µ = 40 and σ = 18 a. describe the distribution of sample means based on samples of n = 36 selected from this population (shape, central tendency,

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Question 387293: A distribution of scores has µ = 40 and σ = 18
a. describe the distribution of sample means based on samples of n = 36 selected from this population (shape, central tendency, variability)
b. of all the possible samples of n = 36, what proportion will have sample means greater than 43?
c. of all the possible samples of n = 36, what proportion will have sample means less than 34?

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a. n = 36, this is considered a large sample. For large samples, the Central Limit Theorem says that the distribution of the sample means is approximately normal (getting better as n gets higher and higher). The mean is mu+=+40and the variance %28%28sigma%29_X%29%5E2+=+sigma%5E2%2Fn.
b. P%28X+%3E+43%29+=+P%28%28X+-+40%29%2F%2818%2Fsqrt%2836%29%29+%3E+%2843+-+40%29%2F3+=+1%29. Hence P%28X+%3E+43%29+=+P%28Z+%3E+1%29+=+0.1587.
c. P%28X+%3C+34%29+=+P%28%28X+-+40%29%2F%2818%2Fsqrt%2836%29%29%3E+%2834+-+40%29%2F3+=+-2%29. Hence P%28X+%3C+34%29+=+P%28Z+%3C+-2%29+=+0.0228.