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Answer :
a) Percentage of people weighing less than 135 lb is 10.56% , b) percentage of weights between 150 and 190 lb is 0.6247 or about 62.47%, c) 30th percentile weight is is 149.6 lb.
a) To find the percentage of people weighing less than 135 lb, we first calculate the Z-score.
Z-score = (X - Mean) / SD = (135-160) / 20 = -1.25. Using a standard Z-score table, the area corresponding to this Z-score is approximately 0.1056, or 10.56% of people weigh less than 135 lb.
b) To find the percentage of weights between 150 and 190 lb, we similarly find the Z-scores for both weights. For 150 lb,
Z-score = (150-160) / 20 = -0.5. For 190 lb, Z-score = (190-160) / 20 = 1.5.
Using a Z-score table, the areas corresponding to these scores are approximately 0.3085 for -0.5 and 0.9332 for 1.5.
So,the percentage of weights between 150 and 190 lb is 0.9332 - 0.3085 = 0.6247, or about 62.47%.
c)The 30th percentile weight corresponds to a Z-score of approximately -0.52. Using the formula Weight = Z(SD) + Mean, we find the 30th percentile weight to be approximately -0.52(20) + 160 = 149.6 lb.
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