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 closest to _______.
A)0.9544
B)0.6826
C)0.8185
D)0.5899
E)0.0897

Question

Quizplus · Accepted Answer

The standard deviation of the population is the square root of the variance, which is sqrt(8100) = 90. The standard error of the mean (SEM) for a sample size of 36 is the standard deviation divided by the square root of the sample size, which is 90/sqrt(36) = 15. The Z-scores for 840 and 900, given a mean of 870, are (840-870)/15 = -2 and (900-870)/15 = 2, respectively. Looking up these Z-scores in a standard normal distribution table or using a calculator, the probability of being between -2 and 2 standard deviations from the mean is approximately 0.9544.

Suppose a Population Has a Mean of 870 and a Variance