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Answer :
Final answer:
The first quartile of the weight distribution in the statistics class is approximately 135 pounds.
Explanation:
The first quartile of the distribution of weights in this statistics class can be calculated using the z-score formula. The z-score corresponds to the number of standard deviations the quartile value is from the mean. The formula for calculating the z-score is (Q1 - mean) / standard deviation. Substituting the given values, we get (Q1 - 145) / 15 = -0.674. Solving for Q1, we find that the first quartile is approximately 135 pounds.
Learn more about Calculating Quartiles here:
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Final answer:
The first quartile of the weights in a large statistics class with a mean weight of 145 pounds and standard deviation of 15 pounds is approximately 135.375 pounds - this indicates that about 25% of students weigh less than this.
Explanation:
In the field of statistics, a quartile represents a type of quantile which divides the number of data points into four more or less equal parts, or quarters. The first quartile, also known as the lower quartile, is the value below which lies the 25 percent of the data. In a normal distribution, the first quartile is located approximately at a distance of 0.675 standard deviations below the mean.
In this particular case, with a mean weight of 145 pounds and a standard deviation of 15 pounds, you can calculate the approximate weight of the first quartile by subtracting 0.675 times the standard deviation from the mean:
145 - 0.675*15 ≈ 135.375 pounds
This means that approximately 25% of students in this very large statistics class weigh less than approximately 135.375 pounds.
