Answer:
Probability that the sample mean score is less than 522 = 0.0166 .
Step-by-step explanation:
We are given that in 2010 the mean mathematics SAT score was 555, and the standard deviation was 125 i.e.;
Mean, [tex]\mu[/tex] = 555 and Standard deviation, [tex]\sigma[/tex] = 125
Also, Z = [tex]\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1) where, X bar = sample mean
n = sample size
Now, Probability(X bar < 522) = P( [tex]\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{522-555}{\frac{125}{\sqrt{65} } }[/tex] ) = P(Z < -2.1284)
= P(Z > 2.1284) = 0.0166
The above probability is calculated using z table.
Therefore, the probability that the sample mean score is less than 522 is 0.0166 .
