Respuesta :
Answer:
[tex]z=\frac{4415-3400}{450}=2.26[/tex]
And the explanation of this number is:"The number of text messages for Kendra it's 2.26 deviations above the mean"
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Calculate the z score
Let X the random variable that represent the number of text messages per month, and for this case we know the distribution for X is given by:
[tex]X \sim N(3400,450)[/tex]
Where [tex]\mu=3400[/tex] and [tex]\sigma=450[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]z=\frac{4415-3400}{450}=2.26[/tex]
And the explanation of this number is:"The number of text messages for Kendra it's 2.26 deviations above the mean"
