Find the indicated probability or percentage for the sampling error.
-Scores on a biology final exam are normally distributed with a mean of 220 and a standard deviation of 24. Determine the percentage of samples of size 9 that will have mean scores within 12
Points of the population mean score of 220.
A)86.64%
B)13.36%
C)93.32%
D)38.30%

Question

Find the indicated probability or percentage for the sampling error.
-Scores on a biology final exam are normally distributed with a mean of 220 and a standard deviation of 24. Determine the percentage of samples of size 9 that will have mean scores within 12
Points of the population mean score of 220. 
A)86.64%
B)13.36%
C)93.32%
D)38.30%

Quizplus · Accepted Answer

The standard error of the mean (SEM) for samples of size 9 is 24/sqrt(9) = 8. The z-scores for 12 points above and below the mean are (232-220)/8 = 1.5 and (208-220)/8 = -1.5. The probability of a z-score between -1.5 and 1.5 is approximately 86.64%.

Find the Indicated Probability or Percentage for the Sampling Error