A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is
A)0.4332
B)0.8664
C)0.9332
D)0.0668

Question

Quizplus · Accepted Answer

The standard error of the mean is 18/sqrt(144) = 1.5. Using the standard normal distribution, the z-scores for 297 and 303 are (297-300)/1.5 = -2 and (303-300)/1.5 = 2. The probability of a z-score between -2 and 2 is approximately 0.8664.

A Population Has a Mean of 300 and a Standard