Question

Law firm averages 149 cases per year with a standard deviation of 14 points. Suppose the law firm's cases per year are normally distributed. Let X= the number of cases per year. Then X∼N(149,14). Round your answers to THREE decimal places.

Answer 1

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

Answer 2

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:

`X \sim N(149,14)`

Where
`\mu=149` and
`\sigma=14`

The z score formula is given by:

`z=(x-\mu)/(\sigma)`

The z score for X=186 is:

`z = (186-149)/(14)= 2.643`

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

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:

`X \sim N(149,14)`

Where
`\mu=149` and
`\sigma=14`

The z score formula is given by:

`z=(x-\mu)/(\sigma)`

The z score for X=186 is:

`z = (186-149)/(14)= 2.643`

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