Assume the weight of all adults in the United States is normally distributed with a mean of 160 lbs and a standard deviation of 15 lbs. If person A weighs 145 lbs, which part under the normal curve should be shaded if we want to know the percentage of people heavier than person A?

First, we need to calculate the z-score for person A's weight. The z-score measures the number of standard deviations person A's weight is away from the mean.

The formula to calculate the z-score is:

z = (x - μ) / σ

Where:

- x is the value we want to convert to a z-score (person A's weight)

- μ is the mean of the distribution (160 lbs)

- σ is the standard deviation of the distribution (15 lbs)

Substituting the values:

z = (145 - 160) / 15

z = -1

Now, we need to find the area to the right of the z-score of -1 on the standard normal distribution table or using a calculator.

The area to the right of z = -1 is equal to the area to the left of z = 1 (since the total area under the curve is 1).

Using a standard normal distribution table or calculator, we find that the area to the left of z = 1 is approximately 0.8413.

Therefore, the percentage of people heavier than person A is approximately 100% - (0.8413100%) = 15.87%.

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