Find the indicated probability or percentage for the sampling error.
-The monthly expenditures on food by single adults living in one neighborhood of Los Angeles are normally distributed with a mean of $370 and a standard deviation of $80. Determine the
Percentage of samples of size 4 that will have mean monthly expenditures on food within $72 of
The population mean expenditure of $370.
A)46.41%
B)96.41%
C)63.18%
D)92.82%

Question

Find the indicated probability or percentage for the sampling error.
-The monthly expenditures on food by single adults living in one neighborhood of Los Angeles are normally distributed with a mean of $370 and a standard deviation of $80. Determine the
Percentage of samples of size 4 that will have mean monthly expenditures on food within $72 of
The population mean expenditure of $370. 
A)46.41%
B)96.41%
C)63.18%
D)92.82%

Quizplus · Accepted Answer

The standard error for a sample size of 4 is $80/√4 = $40. The z-scores for $72 above and below the mean are ($370±$72-$370)/$40 = ±1.8. The probability of a z-score between -1.8 and 1.8 is approximately 92.82%.

Find the Indicated Probability or Percentage for the Sampling Error