The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.2 minutes and standard deviation 1.5 minutes. Suppose that a random sample of n = 49 customers is observed. Find the probability that the average waiting time in line for these customers is

Part a

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

Part b

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

Part c

And using 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 time waiting at an airport check in of a population, and for this case we know the distribution for X is given by:

Where and

We select a random sample of n = 49. Since the distribution of X is normal then the distribution for the sample mean is also normal and given by:

We can find the individual probabilities like this:

Part a

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

Part b

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

Part c

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

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