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Step-by-step explanation:
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Assuming a mean of $204 per night and a deviation of $55.
a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)?
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".
Let X the random variable that represent the cost per night at the hotel, and for this case we know the distribution for X is given by:
Where and
And let represent the sample mean, the distribution for the sample mean is given by:
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way: