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The mean of a dataset is 80 and standard deviation of 5. Approximately what percentage of...

The mean of a dataset is 80 and standard deviation of 5. Approximately what percentage of data is between 65 and 95?The mean of a dataset is 80 and standard deviation of 5. Approximately what percentage of data is between 65 and 95?

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Answer #1

The mean of a data set is 80, and the standard deviation is 5.

We have to find the percentage of data that falls between 65 and 95.

So, if the corresponding random variable is X, then X follows Normal with mean 80 and standard deviation of 5.

So, we can say that

Z=(X-80)/5 follows standard normal with mean 0 and standard deviation 1.

We have to find

Where, phi is the distribution function of the standard normal variate.

From the standard normal table, this becomes

So, the corresponding percentage is 0.9974*100, ie. 99.74%.

So, the answer is 99.74%.

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