Question

Assume that the average annual salary for a worker in the United States is $35,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to 6,500. Find the following:

A-What percentage of Americans earn below $26,000.
B- What percentage of Americans earn below $26,000.

Answer 1

$$\mathrm{E} = 35000$$ $$\mathrm{D} = 6500$$

x- random variable- represents salary.

$$\mathrm{P}(x < 26000) = \mathrm{P}\left(\frac{E - x}{d} < \frac{E - 26000}{d}\right) = \text{by Central Limit Thereme} = \mathrm{F}\left(\frac{35000 - 26000}{6500}\right) = \mathrm{F}(1.38) = 0.9162$$