Answer :
Answer:
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(149,14)[/tex]
Where [tex]\mu=149[/tex] and [tex]\sigma=14[/tex]
The z score formula is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
The z score for X=186 is:
[tex] z = \frac{186-149}{14}= 2.643 [/tex]
The z-score when x=186 is 2.643 . This z-score tells you that x=186 is 2.643 standard deviations to the right of the mean, which is 186 +2.643*14= 223.002
Step-by-step explanation:
Assuming the following question:
Suppose the law firm has 186 cases in 2015. The z-score when x=186 is ___ . This z-score tells you that x=186 is ___ standard deviations to the right of the mean, which is ___
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 heights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(149,14)[/tex]
Where [tex]\mu=149[/tex] and [tex]\sigma=14[/tex]
The z score formula is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
The z score for X=186 is:
[tex] z = \frac{186-149}{14}= 2.643 [/tex]
The z-score when x=186 is 2.643 . This z-score tells you that x=186 is 2.643 standard deviations to the right of the mean, which is 186 +2.643*14= 223.002
Answer: the z- score when x= 186 is 2.643
the mean is 149
this z score tells you that x= 186 is 2.643 standard dev. to the right of the mean