Answer :
To find the probability that a 10 year old child is under 51.7 inches, we calculate the z-score which is -0.5. On referring to the z-table, the probability associated with this z-score is approximately 0.3085 or 30.85%.
The subject of the question is Mathematics, more specifically, Statistics. To find the probability that a randomly chosen 10 year old child is less than 51.7 inches, we need to convert the height into a z-score. The z-score is a measure of how many standard deviations an element is from the mean. This is calculated using the formula:
z = (x - μ) / σ
Where 'x' is the value (51.7), 'μ' is the mean (55.1), and 'σ' is the standard deviation (6.8).
So, the z-score would be:
z = (51.7 - 55.1) / 6.8 = -0.5
The next step is to use the standard normal distribution table or calculator to find the probability associated with this z-score. The probability that a z-score is less than -0.5 is approximately 0.3085 or 30.85%. So the probability that a randomly chosen 10 year old child is less than 51.7 inches is approximated to be 0.3085.
Learn more about the topic of z-table here:
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