We appreciate your visit to In a certain ASU classroom the weight of men has an average of 175 pounds with a standard deviation of 20 pounds Assuming a normal. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Answer:
99.8%
Step-by-step explanation:
Normal Distribution
Standard deviation σ
mean equal to 175 pounds
We should remember approximately values for intervals:
[μ - σ/2 : μ + σ/2] values spread 1σ up and down mean equal to 68.3 %
[μ - σ : μ + σ ] values spread 2σ up and down mean equal to 95.7 %
and finally
[μ - 1.5 σ : μ + 1.5 σ ] values spread 3σ up and down mean equal to 99.7
In our case we were asked porcentage between 4σ (40 kg) spread about mean
175 + 40 = 215
175 - 40 = 135
For that interval we should get 99.8% of values
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Final answer:
To determine the percentage of men weighing between 135 and 215 pounds in a normal distribution with an average of 175 pounds and a standard deviation of 20 pounds, we calculate the z-scores for 135 and 215 pounds. These z-scores fall within ±2 standard deviations from the mean, which encompasses approximately 95% of the data according to the 68-95-99.7 rule for normal distribution.
Explanation:
To find out approximately what percent of men in the ASU classroom weigh between 135 and 215 pounds given that the weight of men is normally distributed with an average of 175 pounds and a standard deviation of 20 pounds, we'll use the properties of a normal distribution.
First, we calculate the z-scores for the weights 135 and 215 pounds to see how many standard deviations away from the mean these values are:
Z for 135 pounds = (135 - 175) / 20 = -2
Z for 215 pounds = (215 - 175) / 20 = 2
According to the 68-95-99.7 rule (empirical rule) for normal distribution, approximately:
68% of the data falls within ±1 standard deviation from the mean.
95% of the data falls within ±2 standard deviations from the mean.
99.7% of the data falls within ±3 standard deviations from the mean.
Since both z-scores of -2 and 2 fall within ±2 standard deviations from the mean, we can infer that approximately 95% of the men in the class weigh between 135 and 215 pounds.
