Question 7

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
750 goblin soldiers.

The Orc Primarch observes that 538 armies have been gathered throughout the nation.
d) Approximately how many armies have higher than 5600 goblin soldiers? Please Show how you got the answer Thank You

269 armies have higher than 5600 goblin soldiers .

Step-by-step explanation:

Step 1: Sketch the curve.

The probability that X>5600 is equal to the blue area under the curve.

Step 2:

Since μ=5600 and σ=750 we have:

P ( X>5600 ) = P ( X−μ > 5600−5600 )=P ( X−μ/σ>5600−5600/750)

Since Z = x−μ/σ and 5600−5600/750=0 we have:

P ( X>5600 )=P ( Z>0 )

Step 3: Use the standard normal table to conclude that:

P (Z>0)=0.5

We have , 538 armies So , armies have higher than 5600 goblin soldiers is :

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Therefore , 269 armies have higher than 5600 goblin soldiers .