Suppose the population of all public Universities shows the annual parking fee per student is normally distributed with a mean of $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a sample mean between $100 and $115 is closest to _______.
A)0.9738
B)0.4738
C)0.0262
D)0.6103
E)0.1103

Question

Quizplus · Accepted Answer

Using the Central Limit Theorem, we can calculate the probability of drawing a sample with a mean between $100 and $115. The standard error (SE) of the sample mean is the population standard deviation divided by the square root of the sample size, which is $18 / \sqrt{49} = $18 / 7 = $2.57. To find the Z-scores for $100 and $115, we use the formula Z = (X - μ) / SE, where X is the sample mean, μ is the population mean, and SE is the standard error. For $100, Z = ($100 - $110) / $2.57 = -3.89. For $115, Z = ($115 - $110) / $2.57 = 1.95. Using the Z-table, the probability of Z being between -3.89 and 1.95 is approximately 0.9738.

Suppose the Population of All Public Universities Shows the Annual