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Date are drawn from a bell-shape distribution with a mean of 170 and a standard deviation of 5. There are 1700 observations in the data set. Approximately what percentage of the data are less than 180?

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pedrocarratore

Answer:

97.73%

Step-by-step explanation:

Mean (μ) = 170

Standard deviation (σ) = 5

Assuming a normal distribution, for any observed value, X, the z-score is determined by:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For X = 180:

[tex]z=\frac{180-170}{5}\\ z=2[/tex]

A z-score of 2 corresponds to the 97.73-th percentile of a normal distribution.

Therefore, the percentage of data that is less than 180 is 97.73%.

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