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Two sprinters, Victor and Aaron, want to find out who has the faster time when compared to each of their teams. Victor has a time of 10.9 seconds, and his team has a mean time of 11.4 seconds and a standard deviation of 0.2 seconds. Aaron has a time of 10.6 seconds, and his team has a mean of 11.5 seconds and a standard deviation of 0.1 seconds. Who has the faster time when compared to each of their teams

Sagot :

Answer:

The answer is "-9".

Step-by-step explanation:

[tex]\mu = 11.4\\\\\sigma = 0.2\\\\ x = 10.9\\\\[/tex]

[tex]P(X <= 10.9)=?[/tex]

The z-value is determined using the central boundary theorem

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

  [tex]= \frac{(10.9 - 11.4)}{0.2}\\\\ = -2.5[/tex]

Calculating the value for Aaron

[tex]\mu = 11.5\\\\ \sigma = 0.1\\\\ x = 10.6\\\\ P(X <= 10.6)=?[/tex]

When the z-value is calculated using Central Limit Theorem

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

  [tex]= \frac{(10.6 - 11.5)}{0.1}\\\\ = -9[/tex]

Answer:

The times are equal when compared to each of their teams.

Step-by-step explanation:

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