Final answer:
The probability of a randomly chosen ten-year-old child being less than 45.25 inches tall in the United States of Heightlandia is found using the Z-score method. The calculation leads to a probability of approximately 5.62%, which does not match the options given in the question. There may be an error in the calculation or options provided.
Step-by-step explanation:
The probability that a randomly chosen ten-year-old child in the United States of Heightlandia has a height of less than 45.25 inches can be found using the standard normal distribution (Z-score). First, we calculate the Z-score using the formula Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. In this situation, X = 45.25 inches, μ = 55.3 inches, and σ = 6.3 inches.
Plugging in the values, we get Z = (45.25 - 55.3) / 6.3 = -10.05 / 6.3 = -1.5873. Next, we use the Z-score to find the cumulative probability from the standard normal distribution table or a calculator, which represents the probability of a child being shorter than 45.25 inches. The closest value to -1.5873 in the Z-table corresponds to the probability of 0.0562 or 5.62%. Since the values in the Z-table are for the positive side, we consider the other side of the distribution, which gives us 1 - 0.0562 = 0.9438 or 94.38%. Hence, the probability that a randomly chosen child is less than 45.25 inches tall is approximately 0.0562 or 5.62%, which is not among the options provided (a-d). There might be a mistake in the calculation or a typo in the options provided.