Respuesta :
Answer:
Let X the random variable that represent the miles per gallon in cars of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(30,2)[/tex]
Where [tex]\mu=30[/tex] and [tex]\sigma=2[/tex]
We can calculate the coeffcient of variation for this cae like this:
[tex] CV= \frac{\sigma}{\bar X}= \frac{2}{30}= 0.0667=6.7\%[/tex]
Let Y the random variable that represent the miles per gallon in trucks of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(17,3)[/tex]
Where [tex]\mu=17[/tex] and [tex]\sigma=3[/tex]
We can calculate the coeffcient of variation for this cae like this:
[tex] CV= \frac{\sigma}{\bar X}= \frac{3}{17}= 0.176=17.6\%[/tex]
So then we can conclude that the mpg for trucks have more variation since the coefficient of variation is larger than the value obtained for cars.
Step-by-step explanation:
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".
Solution to the problem
Let X the random variable that represent the miles per gallon in cars of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(30,2)[/tex]
Where [tex]\mu=30[/tex] and [tex]\sigma=2[/tex]
We can calculate the coeffcient of variation for this cae like this:
[tex] CV= \frac{\sigma}{\bar X}= \frac{2}{30}= 0.0667=6.7\%[/tex]
Let Y the random variable that represent the miles per gallon in trucks of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(17,3)[/tex]
Where [tex]\mu=17[/tex] and [tex]\sigma=3[/tex]
We can calculate the coeffcient of variation for this cae like this:
[tex] CV= \frac{\sigma}{\bar X}= \frac{3}{17}= 0.176=17.6\%[/tex]
So then we can conclude that the mpg for trucks have more variation since the coefficient of variation is larger than the value obtained for cars.
