Suppose that cars arrive at the Burger King’s drive-through at the rate of 20 cars every hour between noon and 1:00 PM. A random sample of 40 one-hour time periods between noon and 1:00 PM is selected and has a mean of 22.1 cars arriving. Assume that µ = 20 and that σ = √20 for the population of cars arriving at Burger King. What is the probability that a simple random sample of 40 one-hour time periods results in a mean of at least 22.1 cars?

And using the complement rule and a calculator, excel or the normal standard table we have that:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

Where and

Since the distribution for X is normal then the distribution for the sample mean is given by:

We want to find this probability:

And we can use the z score given by:

And replacing we got

We can find the individual probabilities like this:

And using the complement rule and a calculator, excel or the normal standard table we have that:

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step-by-step explanation: