The z score for a per - day expense of $400 is 0.65 while about 84.13% of the hotels is greater than $268
The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\\mu=mean,x=raw\ score,\sigma=standard \ deviation\\\\Given\ that:\\\\\mu=348,\sigma=80[/tex]
a) For an expense of $400:
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{400-348}{80}\\\\z=0.65[/tex]
The z score for a per - day expense of $400 is 0.65
b) For an expense greater than $268:
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{268-348}{80}\\\\z=-1[/tex]
P(x > 268) = P(z > -1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413 = 84.13%
About 84.13% of the hotels is greater than $268
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