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Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man 63.8 inches tall. ( round to 2 decimal places)



Answer :

jacob193

Answer:

Approximately [tex](-1.86)[/tex].

Step-by-step explanation:

In a distribution of mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the [tex]z[/tex]-score of an observed value [tex]x[/tex] is:

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

In this question:

  • The mean of the distribution is [tex]\mu = 69.0[/tex] inches.
  • The standard deviation of the distribution is [tex]\sigma = 2.8[/tex] inches.
  • The observed value is [tex]x = 63.8[/tex] inches.

Hence, the [tex]z[/tex]-score for the observed value [tex]x = 63.8[/tex] would be:

[tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{63.8 - 69.0}{2.8} \approx -1.86[/tex].

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