Answer:
For the restaurant that charges 95 cents, the z-score is -4.29.
For the restaurant that charges $1, the z-score is -3.57.
For the restaurant that charges $1.35, the z-score is 1.43
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 p-value, we get the probability that the value of the measure is greater than X.
The average cost of a glass of iced tea is $1.25 with a standard deviation of 7c.
This means that [tex]\mu = 1.25, \sigma = 0.07[/tex]
Restaurant that charges 95 cents:
The z-score is found when X = 0.95. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.95 - 1.25}{0.07}[/tex]
[tex]Z = -4.29[/tex]
For the restaurant that charges 95 cents, the z-score is -4.29.
Restaurant that charges $1:.
X = 1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1 - 1.25}{0.07}[/tex]
[tex]Z = -3.57[/tex]
For the restaurant that charges $1, the z-score is -3.57.
Restaurant that charges $1.35:
X = 1.35
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.35 - 1.25}{0.07}[/tex]
[tex]Z = 1.43[/tex]
For the restaurant that charges $1.35, the z-score is 1.43