Suppose the population of all public Universities shows the annual parking fee per student is $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 mean of more than $115 is _______.
A) 0.9738
B) 0.4738
C) 0.0262
D) 0.6103
E) 0.1103

Question

Quizplus · Accepted Answer

We can use the central limit theorem to determine the probability of drawing a sample with a mean of more than $115. 
The sample size (n) is 49, which is greater than 30, so the sample mean will be approximately normally distributed. 
The mean of the sampling distribution of the sample means will be equal to the population mean, which is $110. 
The standard deviation of the sampling distribution of the sample means, also known as standard error, will be equal to the population standard deviation divided by the square root of the sample size, which is 18/sqrt(49) = 2.571. 
Now we can standardize the sample mean:

Z = (X - μ) / (σ / sqrt(n)) 
Z = (115 - 110) / (18/sqrt(49)) 
Z = 2.193

Using a standard normal distribution table or calculator, we can find the probability of Z being greater than 2.193:

P(Z > 2.193) = 0.0156

Therefore, the probability of drawing a sample with a mean of more than $115 is 0.0156 or approximately 0.0262 (rounded to four decimal places), which corresponds to choice C.

Suppose the Population of All Public Universities Shows the Annual