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Carrie and Vicki are both enthusiastic players of a certain computer game. Over the past year, Carrie’s mean score when playing the game is 12,400 with a standard deviation of 1500. During the same period, Vicki’s mean score is 14,200, with a standard deviation of 2000. They devise a fair contest: each one will play the game once, and they will compare z-scores. Carrie gets a score of 14,000, and Vicki gets a score of 16,000. Calculate their z-scores and determine who won the contest.

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Answer:

Carrie won

Step-by-step explanation:

Carrie's mean 12,400 and standard deviation 1,500.

Vicki's mean 14,200 and standard deviation 2,000.

Z score is the distant a value is from the mean in terms of standard deviations.

[tex]z = \frac{x-\mu}{\sigma}[/tex]

x is the value

μ is the mean

σ is the standard deviation

Carrie's z-score:

[tex]z = \frac{14,000-12,400}{1,500}=1.07[/tex]

Vicki's z-score:

[tex]z = \frac{16,000-14,200}{2,000}=0.9[/tex]

Comparing z-score Carrie won the contest

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