# probability and statistics

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the population of sat scores forms a normal distribution with a mean of u=500 and a standard deviation of o=100. if the average sat score is calculated for a sample of n=25 students.
a. what is the probability that the sample mean will be greater than m=510? in symbols, what is p(m>510)?
b. what is the probability that the sample mean will be greater than m=520? in symbols, what is p(m>520)?
c. what is the probability that the sample mean will between m=510 and m=520? in symbols, what is p(510<m<520)?

• probability and statistics -

Z = (score-mean)/SEm

SEm = SD/√n

Treat the new mean as a score.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.

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