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Answer :
Final answer:
To find the probability that a person's weight is greater than 158 pounds, we calculate the z-score and use the standard normal distribution table.
Explanation:
To find the probability that a person's weight is greater than 158 pounds, we need to calculate the z-score and then use the standard normal distribution table.
The z-score is calculated using the formula z = (x - mean) / standard deviation. In this case, the mean is 165 pounds and the standard deviation is 31 pounds.
So, the z-score is z = (158 - 165) / 31 = -0.226.
Using the standard normal distribution table, we can find that the probability of a z-score less than -0.226 is approximately 0.409. Therefore, the probability of a person randomly selected having a weight greater than 158 pounds is 1 - 0.409 = 0.591.
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