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27.03.2021 •
Mathematics
The weight of adult female panthers in one habitat area are normally distributed with a mean of 82 pounds and a standard deviation of 9.8 pounds. What percent of the panthers weigh less than 76 pounds?
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Ответ:
27.09% of the panthers weigh less than 76 pounds
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 82 pounds and a standard deviation of 9.8 pounds.
This means that![\mu = 82, \sigma = 9.8](/tpl/images/1225/3688/98deb.png)
What percent of the panthers weigh less than 76 pounds?
The proportion is the pvalue of Z when X = 76. So
0.2709*100% = 27.09%
27.09% of the panthers weigh less than 76 pounds
Ответ:
Till then. -ayeitswesley