Answer:
We can use the z score formula given by:
If we use this formula we got:
And using a calculator, excel or the normal standard table and we have that:
Step-by-step explanation:
We assume this previous info: It is known that the amounts of time required for room-service delivery at a certain Marriott Hotel are Normally distributed with the average delivery time of 20 minutes.
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 delivery times 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:
And we can use the z score formula given by:
If we use this formula we got:
And using a calculator, excel or the normal standard table and we have that: