Question

Question 9
Orc leaders need to gather armies to fight in an upcoming war. The army sizes are
normally distributed with a mean of 5600 goblin soldiers and a standard deviation of
750 goblin soldiers.


In the world of Orcs, if an Orc Leader shows up with an army of a z-score lower than
-1.5, he is immediately executed and another leader is chosen. Brutal, right?


Part A: Lord Barbaroid, an Orc Leader, appears with an army of 4400 goblin soldiers.
Based on the Orc Rule, will he be executed? Please state his Z-score, show all work
as to how you got your answer, and whether he will die to obtain full credit!

Part B: How many more goblin soldiers would Lord Barbaroid have needed in order
to NOT be executed and meet that Z-Score? Please state the raw score needed to
NOT be executed and how far away Lord Barbaroid was from that army size. Show
all work Please Thank You ​

Answer 1

Answer:

Part A) Barbaroid will be executed

Part B) 75 more globin soldiers

Step-by-step explanation:

The army sizes of ORC leaders are

normally distributed with a mean of 5600 goblin soldiers and a standard deviation of 750 goblin soldiers.

The rule is that, if an Orc Leader shows up with an army of a z-score lower than

-1.5, he is immediately executed.

We want to determine whether Lord Barbaroid, an Orc Leader, who appears with an army of 4400 goblin soldiers,

based on the Orc Rule, will he be executed or not.

We find the z-score corresponding to 4400 using

$z = \frac{x - \mu}{ \sigma}$

We substitute x=4400 , the standard deviation and the mean to get:

$z = \frac{4400 - 5600}{750} = - 1.6$

Since Lord Barbaroid's z-score , -1.6 is less than -1.5 he will be executed.

Part B)

We want to find how many more goblin soldiers Lord Barbaroid have needed in order to NOT be executed and meet that Z-Score.

So we need to find the number of globin soldiers that corresponds to -1.5.

$- 1.5 = \frac{x - 5600}{750}$

$750 \times - 1.5 = x - 5600$

$- 1125 = x - 5600 \\ x = 5600 - 1125$

$x = 4475$

Therefore Barbaroid needed 4475-4400=75 more globin soldiers.