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Answer :
The probability that one randomly selected adult male has a weight greater than 144 pounds is approximately 86.43%.
We will use the Z-score formula:
[tex]Z = (X - mu\) / sigma\[/tex]
Where X is the value we are interested in (144 pounds), \\mu\ is the mean (176 pounds), and \\sigma\ is the standard deviation (29 pounds).
Calculating the Z-score gives us:
[tex]Z = (144 - 176) / 29\\Z = -32 / 29\\Z approx\ -1.10[/tex]
Now, we will consult the standard normal distribution (Z-distribution) table or use a calculator with normal distribution functions to find the probability that Z is greater than -1.10. The table or calculator will provide the area to the right of the Z-score, which corresponds to the probability.
The Standard Normal Distribution table indicates that the probability for Z > -1.10 is approximately 0.8643 or 86.43%. Therefore, there is an 86.43% chance that a randomly selected adult male weighs more than 144 pounds.
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