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.)

Answer

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Answer

B) Answer: \( = 0.001 \)

Steps

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: \( = 0.001 \)