Sure! I'll solve your questions step by step, just like the example. --- ## **Given Data** - Mean (\(\mu\)): 60 - Standard deviation (\(\sigma\)): 6.9 --- ## **(a) Probability that an elite athlete has a maximum oxygen uptake of at least 55 ml/kg** **Step 1: Z-score Calculation** \[ P(X \geq 55) = 1 - P(X < 55) \] \[ Z = \frac{55 - 60}{6.9} = \frac{-5}{6.9} \approx -.7246 \] **Step 2: Find cumulative probability** \[ P(X < 55) = P(Z < -.7246) \] From Z-table or Excel: \[ P(Z < -.7246) \approx .2347 \] **Step 3: Final probability** \[ P(X \geq 55) = 1 - .2347 = .7653 \] **Answer:** \[ \boxed{.7653} \] --- ## **(b) Probability that an elite athlete has a maximum oxygen uptake of 60 ml/kg or lower** **Step 1: Z-score Calculation** \[ P(X \leq 60) \] \[ Z = \frac{60 - 60}{6.9} = \] **Step 2: Find cumulative probability** \[ P(X \leq 60) = P(Z \leq ) = .5 \] **Answer:** \[ \boxed{.5} \] --- ## **(c) Someone with a maximum oxygen uptake of 25 ml/kg. Is it likely this person is an elite athlete?** **Step 1: Z-score Calculation** \[ Z = \frac{25 - 60}{6.9} = \frac{-35}{6.9} \approx -5.072 \] This Z-score is **very far** below the mean. A Z-score below -3 is extremely rare (less than .13%). **Conclusion:** \[ \boxed{\text{NO}} \] --- ### **Summary Table** | Question | Probability / Answer | |----------|---------------------| | (a) | .7653 | | (b) | .5 | | (c) | NO | --- **Let me know if you need the explanations for the Excel formula or additional steps!**