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 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 approximate the sampling distribution of the sample mean:

μx̄ = μ = $110
σx̄ = σ/√n = $18/√49 = $2.57

We want to find the probability of drawing a sample with a mean of more than $115:

P(x̄ > $115) = P(z > (115 - 110)/2.57) = P(z > 1.95)

Using a standard normal table or calculator, we find:

P(z > 1.95) = 0.0262

Therefore, the probability of drawing a sample with a mean of more than $115 is 0.0262 or 2.62%, which corresponds to choice (C).

Suppose the Population of All Public Universities Shows the Annual