Final answer:
Using the z-score calculation and the standard normal distribution table, there is a 19.62% chance that a randomly selected ten-year-old child in Heightlandia will be shorter than 49.1 inches.
Step-by-step explanation:
To find the probability that a randomly chosen child in the United States of Heightlandia has a height of less than 49.1 inches, we first calculate the z-score, which is the number of standard deviations a value is away from the mean.
The formula for the z-score is: Z = (X - μ) / σ
Where X is the value in question, μ is the mean, and σ is the standard deviation. Let's calculate it:
Z = (49.1 inches - 56.8 inches) / 9 inches
= -0.85556
Next, we use the standard normal distribution table or a calculator to find the probability that corresponds to a z-score of -0.85556.
The probability associated with a z-score of -0.85556 is approximately 0.1962.
Therefore, there is a 19.62% chance that a randomly selected ten-year-old child from Heightlandia will be shorter than 49.1 inches.