Question

Fuel prices in Vancouver one month had a mean price of $1.34 per liter and a standard deviation of $0.36 per liter. Suppose that we take random samples of 45 prices from this population and calculate the sample mean price for each sample. We can assume that the prices in each sample are independent. What will be the shape of the sampling distribution of the sample mean price

Answer 1

Answer:

The sampling distribution of the sample mean price will be approximately normal with mean $1.34 and standard deviation $0.0537.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

What will be the shape of the sampling distribution of the sample mean price

Mean = $1.34

Standard deviation $s = \frac{0.36}{\sqrt{45}} = 0.0537$

The sampling distribution of the sample mean price will be approximately normal with mean $1.34 and standard deviation $0.0537.