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Suppose a 15 to 18-year-old male from Chile was 176 cm tall from 2009 to 2010.

The z-score when \( x = 176 \) cm is \( z = \) _______.

This z-score tells you that \( x = 176 \) cm is ________ standard deviations to the ________ (right or left) of the mean.

(What is the mean?)

Answer :

Answer:

z = 0.96, standard deviations to the right of the mean 170 cm

Explanation:

z= [tex]\frac{176 - 170}{0.96}[/tex]

x = 176 cm is 0.96, standard deviations to the right of the mean 170 cm

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Rewritten by : Barada

Final answer:

The z-score for a height of 176 cm is approximately 0.96, indicating this height is about 0.96 standard deviations to the right of the mean height of 170 cm for 15 to 18-year-old males from Chile in 2009-2010.

Explanation:

To calculate the z-score for a 15 to 18-year-old male from Chile who was 176 cm tall in 2009-2010, we use the formula: z = (x - μ) / σ, where x is the height of the individual, μ (mu) is the mean height, and σ (sigma) is the standard deviation. Given that the mean height is 170 cm and the standard deviation is 6.28 cm, we can calculate the z-score for a height of 176 cm.

  • z = (176 - 170) / 6.28 = 6 / 6.28 = 0.955414

Therefore, the z-score when x = 176 cm is approximately z = 0.96. This z-score tells you that x = 176 cm is about 0.96 standard deviations to the right of the mean, which is 170 cm.