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Sagot :
Answer:
January had a higher z-score for sales on the 15th, and the value of that z-score was of 0.5.
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.
January:
The mean daily sales for January was $300 with a standard deviation of $20. On the 15th of January, the shop sold $310 of yogurt. This means, respectively, that [tex]\mu = 300, \sigma = 20, X = 310[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{310 - 300}{20}[/tex]
[tex]Z = 0.5[/tex]
February:
The mean daily sales for February was $320 with a standard deviation of $50. On the 15th of February, the shop sold $340 of yogurt. This means, respectively, that [tex]\mu = 320, \sigma = 50, X = 340[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{340 - 320}{50}[/tex]
[tex]Z = 0.4[/tex]
January had a higher z-score for sales on the 15th, and the value of that z-score was of 0.5.
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