Respuesta :
Answer:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(58,21)[/tex]
Where [tex]\mu=58[/tex] and [tex]\sigma=21[/tex]
The z score for this case is given by this formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:
[tex] X= \mu +1.78 \sigma= 58 +1.78*21= 95.38[/tex]
So the corresponging weight for a z score of 1.78 is 95.38 grams
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 weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(58,21)[/tex]
Where [tex]\mu=58[/tex] and [tex]\sigma=21[/tex]
The z score for this case is given by this formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:
[tex] X= \mu +1.78 \sigma= 58 +1.78*21= 95.38[/tex]
So the corresponging weight for a z score of 1.78 is 95.38 grams
