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A distribution of measurements is bell-shaped
with a mean of 60 and a standard deviation of 12. Use this information to find the proportion of measurements
in the given interval.
greater than 72
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The task embarrasses to say it directly, but hints at it figuratively that the distribution is normal.
Certainly, we are smart enough and understand this hidden allegory correctly.
72 is two standard deviation from the mean 60.
Use the relevant empirical rule, which says that 95% of data are within two standard deviations.
Hence, 5% are out of the two standard deviations.
Due to the symmetry of the normal distribution, it means that half of that, or 2.5%, is above 72.
ANSWER. 2.5% of measurements are above 72.
Solved.