If the amount of petrol purchased per car at a large petrol station has a population mean of $15 and a population standard deviation of $4 and a random sample of 4 cars is selected,there is approximately a 68.26% chance that the sample mean will be between $13 and $17.

Question

Quizplus · Accepted Answer

To determine the probability of the sample mean being between $13 and $17, we need to calculate the standard error of the mean (SEM) first:
SEM = sd/sqrt(n) = 4/sqrt(4) = 2

Then, we can calculate the z-scores for $13 and $17:
z1 = (13-15)/2 = -1
z2 = (17-15)/2 = 1

Using a standard normal distribution table or calculator, we can find the probability of the sample mean falling between these z-scores:
P(-1<z<1) = 0.6827

However, this is only an approximation based on the central limit theorem, since the population standard deviation is known and the sample size is small. In reality, the distribution of petrol purchased per car may not be normally distributed, and the sample mean could fall outside of the given range with a higher or lower probability. Therefore, the statement is false.

If the Amount of Petrol Purchased Per Car at a Large