# A data set with roughly a bell-shaped distribution has mean 45 and standard deviation 12. Approximately what percentage of the observations lie between 33 and 57?

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A data set with roughly a bell-shaped distribution has mean 45 and standard deviation 12. Approximately what percentage of the observations lie between 33 and 57?

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Step 1

The percentage of the observations lie between 33 and 57 is obtained below:

Let X be an observation from a bell shaped distribution, having mean x-bar and sample standard deviation s, then according to the 68-95-99.7-rule, approximately 68%, 95% and 99.7% of the values lie within one, two and three standard deviations of the mean respectively. That is,

Step 2

It is given that the distribution is roughly a bell-shaped with mean is 45 and standard deviation is...

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