A waiter believes that his tips from various customers have a slightly right skewed distribution with a mean of 10 dollars and a standard deviation of 2.50 dollars. What is the probability that the average of 35 customers will be more than 13 dollars

And we can use the z score given by:

And replacing we got:

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

We select a sample size n = 35, and we know that the distribution for the sample mean is given by:

We want to find the following probability:

And we can use the z score given by:

And replacing we got:

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

mx+89b(-98)nb

step-by-step explanation: