Suppose a population has a mean of 870 and a variance of 8,100.If a random sample of size 36 is drawn from the population,the probability that the sample mean is between 840 and 900 is _______.
A) 0.9544
B) 0.6826
C) 0.8185
D) 0.5899
E) 0.0897

Question

Quizplus · Accepted Answer

The standard deviation of the sample mean is the population standard deviation divided by the square root of the sample size: sqrt(8100/36) = 15. The z-scores for 840 and 900 are (840-870)/15 = -2 and (900-870)/15 = 2, respectively. The probability of a z-score between -2 and 2 is approximately 0.9544.

Suppose a Population Has a Mean of 870 and a Variance