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.

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:

Where and

The z score formula is given by:

The z score for X=186 is:

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:

Where and

The z score formula is given by:

The z score for X=186 is:

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

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!