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 it is assumed that the amount of petrol purchased per car is symmetric,there is approximately a 68.26% chance that a random sample of 16 cars will have a sample mean between $14 and $16.

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the distribution of the sample means. From the information given, we know that the population mean is μ = $15 and the population standard deviation is σ = $4.

The standard error of the mean is σ/√n = $4/√16 = $1.

To find the probability that a random sample of 16 cars will have a sample mean between $14 and $16, we need to find the z-scores for these values:

z1 = ($14 - $15) / $1 = -1

z2 = ($16 - $15) / $1 = 1

Using a standard normal distribution table or calculator, we can find that the probability of a z-score between -1 and 1 is approximately 0.6826, or 68.26%. Therefore, the statement is true.

If the Amount of Petrol Purchased Per Car at a Large