The probability that a randomly selected datum falls within 2 standard deviations of the mean as required is; 0.95.
What is the probability that a datum falls within 2 standard deviations of the mean?
By observation, it follows that the distribution as represented in the task content above is a normal distribution.
On this note, the empirical rule applies as follows;
For a standard normal distribution, 68% of the observations (datum) fall within 1 standard deviation of the mean; 95% of the datum lie within two standard deviation of the mean; and 99.9% lie within 3 standard deviations of the mean.
On this note, when expressed as a percentage; the probability that the randomly selected datum falls with 2 standard deviations is; 95/100 = 0.95.
Read more on normal distribution;
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