Question

SAT Scores: Assume that in 2010 the mean mathematics SAT score was 555, and the standard deviation was 125. A sample of 65 scores is chosen. Use the Ti-84 calculator. What is the probability that the sample mean score is less than 522?

Answer 1

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, $\mu$ = 555      and     Standard deviation, $\sigma$ = 125

Also,  Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1) where, X bar = sample mean

                                                        n = sample size

Now, Probability(X bar < 522) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{522-555}{\frac{125}{\sqrt{65} } }$ ) = 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 .