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 64 cars is selected,there is approximately a 95.44% chance that the sample mean will be between $14 and $16.

Question

Quizplus · Accepted Answer

We can use the Central Limit Theorem to approximate the sampling distribution of the sample mean. The mean of the sampling distribution will be the same as the population mean, which is $15. The standard deviation of the sampling distribution, also known as the standard error, can be calculated as:

SE = σ/√n = 4/√64 = 0.5

We want to find the probability that the sample mean falls between $14 and $16. We can standardize the sample mean using the formula:

z = (x - μ)/SE

For x = $14:

z = (14 - 15)/0.5 = -2

For x = $16:

z = (16 - 15)/0.5 = 2

Using a standard normal table, we can find that the probability of obtaining a z-score between -2 and 2 is approximately 0.9544. Therefore, there is approximately a 95.44% chance that the sample mean will fall between $14 and $16.

If the Amount of Petrol Purchased Per Car at a Large