In​ nutrition, the recommended daily allowance of vitamins is a number set by the government to guide an​ individual's daily vitamin intake.​ Actually, vitamin needs vary drastically from person to​ person, but the needs are closely approximated by a normal curve. To calculate the recommended daily​ allowance, the government first finds the standard deviation and the average need for vitamins among people in the population. The recommended daily allowance is then defined as the mean plus 2.2 times the standard deviation. What fraction of the population will receive adequate amounts of vitamins under this​ plan?

Click here to see page 1 of the table for areas under the standard normal curve.
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Click here to see page 2 of the table for areas under the standard normal curve.

The fraction of the population that will receive adequate amounts of vitamins under the given plan is