The SAT has a mean of 500 and a standard deviation of 110 Le

The SAT has a mean of 500 and a standard deviation of 110. Let us assume that the distribution of SAT scores is approximately normal.

a. For a sample of n = 25, what is the probability of getting a sample mean of 480 or lower?

b. For a sample of n = 100, what is the probability of getting a sample mean between 500 and 540?

Solution

(a) P(xbar<480) = P((xbar-mean)/(s/vn) <(480-500)/(110/sqrt(25)))

=P(Z<-0.91) =0.1814 (from standard normal table)

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(b)P(500<xbar<540) = P((500-500)/(110/sqrt(100)) <Z< (540-500)/(110/sqrt(100)))

=P(0<Z<3.64) =0.4999 (from standard normal table)