Question

Naomi weighed 50 patients for a medical study using a scale that measures to the nearest whole pound. She then calculated the mean weight as 176 pounds, with a standard deviation of 12 pounds.
If the distribution is normal, what percent of the data lies between 140 pounds and 212 pounds?

Answer 1

99.7 percentage of the data lies between 140 and 212 pounds when the distribution of the standard deviation is normal.

What is standard deviation?

Any given quantity, which is used to express that how many observations  differ from others in the total observations of a data, is referred to as standard deviation. It is represented by σ.

To calculate the percentage of data lying between the given values, we will use the formula of empirical method and the given information to compute as under,

$\rm P(mu-3\ x\ \sigma < X < \mu + 3\ x\ \sigma)$

Solving further,

$\rm P(176-3\ x\ \12 < X < \176+ 3\ x\ 12) = 0.997$

Hence, the significance upon the standard deviation of data weighted by Naomi is as aforementioned.

Learn more about standard deviation here:

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