Problem
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 54.6 inches, and standard deviation of 6.8 inches. A) What is the probability that a randomly chosen child has a height of less than 60.9 inches? Answer \( = \) (Round your answer to 3 decimal places.) B) What is the probability that a randomly chosen child has a height of more than 74.4 inches? Answer \( = \) (Round your answer to 3 decimal places.)
Solution
Step 1 ：A) Calculate the z-score for height 60.9 inches: \( z = \frac{60.9 - 54.6}{6.8} \)
Step 2 ：A) Find the probability from the z-score: \( P(Z < z) \)
Step 3 ：A) Answer: \( = 0.877 \)
Step 4 ：B) Calculate the z-score for height 74.4 inches: \( z = \frac{74.4 - 54.6}{6.8} \)
Step 5 ：B) Find the probability from the z-score: \( P(Z > z) \)
Step 6 ：B) Answer: \( = 0.001 \)
