Question
In a certain distribution of numbers, the mean is 100 with a standard deviation of 7. At least what fraction of the numbers are between 37 and 163
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Answer to a math question In a certain distribution of numbers, the mean is 100 with a standard deviation of 7. At least what fraction of the numbers are between 37 and 163
Jon
4.6110 Answers
To find the fraction of numbers between 37 and 163, we need to first find the z-scores for these values and then use the z-table to find the corresponding probabilities.
The z-score formula is given by:
z = \frac{x - \mu}{\sigma}
where:
- x
- \mu = 100
- \sigma = 7
For x = 37
z_{37} = \frac{37 - 100}{7} = -9
For x = 163
z_{163} = \frac{163 - 100}{7} = 9
Next, we look up the z-scores -9 and 9 in the z-table. We find that for a z-score of -9, the probability is close to 0, and for a z-score of 9, the probability is close to 1.
Therefore, the fraction of numbers between 37 and 163 is close to 1 (or 100%).
\textbf{Answer:}\frac{100}{100} = 1
The z-score formula is given by:
where:
-
-
-
For
For
Next, we look up the z-scores -9 and 9 in the z-table. We find that for a z-score of -9, the probability is close to 0, and for a z-score of 9, the probability is close to 1.
Therefore, the fraction of numbers between 37 and 163 is close to 1 (or 100%).
\textbf{Answer:}
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