A credit card customer owes $523.85 they are only able to make a payment of $184.50 how much money does the customer still owe?

a)

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

b)

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 interpupillary distance of a population, and for this case we know the distribution for X is given by:

Where  and

Part a

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

We want to find this probability:

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: