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

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

sina-sinb

cosb+cosa

tana-tanb

cos0+cos x pi/3

20tan

step-by-step explanation: