1. **State the problem:** Given a sample of size $n=30$ with scores $X=45$ corresponding to $z=1.50$ and $X=40$ corresponding to $z=1.00$, find the sample mean $M$ and standard deviation $s$. 2. **Recall the formula for z-score:** $$z = \frac{X - M}{s}$$ where $X$ is the score, $M$ is the mean, and $s$ is the standard deviation. 3. **Set up equations from given data:** From $X=45$ and $z=1.50$: $$1.50 = \frac{45 - M}{s} \implies 45 - M = 1.50s$$ From $X=40$ and $z=1.00$: $$1.00 = \frac{40 - M}{s} \implies 40 - M = 1.00s$$ 4. **Subtract the second equation from the first:** $$ (45 - M) - (40 - M) = 1.50s - 1.00s $$ $$ 45 - M - 40 + M = 0.50s $$ $$ 5 = 0.50s $$ 5. **Solve for $s$:** $$ s = \frac{5}{0.50} = 10 $$ 6. **Use $s=10$ in one of the equations to find $M$:** From $40 - M = 1.00s$: $$ 40 - M = 1.00 \times 10 = 10 $$ $$ M = 40 - 10 = 30 $$ 7. **Final answer:** $$ M = 30, \quad s = 10 $$ **Answer choice:** a. $M=30$ and $s=10$