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Answer:
22.96% probability that a hotel room costs between $250.00 and $285.00
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What is the probability that a hotel room costs between $250.00 and $285.00?
This is the pvalue of Z when X = 285 subtracted by the pvalue of Z when X = 250. So
X = 285
has a pvalue of 0.7734
X = 250
has a pvalue of 0.5438
0.7734 - 0.5438 = 0.2296
22.96% probability that a hotel room costs between $250.00 and $285.00