SOLUTION: Assume that the average annual salary for a worker in the United States is $38,000 and that the annual salaries for Americans are normally distributed with a standard deviation equ

Algebra ->  Probability-and-statistics -> SOLUTION: Assume that the average annual salary for a worker in the United States is $38,000 and that the annual salaries for Americans are normally distributed with a standard deviation equ      Log On


   

Question 636624: Assume that the average annual salary for a worker in the United States is $38,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $7,000. Find the following:

(A) What percentage of Americans earn below $25,000?
(B) What percentage of Americans earn above $46,000?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

mean = $38,000  and SD = $7000

(A) What percentage of Americans earn below $25,000? P(z < -1) = (100-68.27)/2 = 15.87%

(B) What percentage of Americans earn above $46,000? P(z > 1) = 15.87%

For the normal distribution: 

one  standard deviation from the mean accounts for about 68.27% of the set 

two standard deviations from the mean account for about 95.4%

and three standard deviations from the mean account for about 99.7%.

Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50%  to the right