SOLUTION: I have no idea of how to approach this word problem. Can you please show me step by step how to solve this problem? The mean IQ score of 1500 students is 100 with a standard dev

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Question 465483: I have no idea of how to approach this word problem. Can you please show me step by step how to solve this problem?
The mean IQ score of 1500 students is 100 with a standard deviation of 15. How many have an IQ between 85 and 115? How many have an IQ between 70 and 130? How many have an IQ of 145?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I have no idea of how to approach this word problem. Can you please show me step by step how to solve this problem?
The mean IQ score of 1500 students is 100 with a standard deviation of 15.
How many have an IQ between 85 and 115?
---
z(85) = (85-100)/15 = -1
z(115) = (115-100)/15 = +1
---
%(85<= x <= 115) = %(-1<= z <=1) = 0.6827
---
# with IQ between 85 and 115 = 0.6827*1500 = 1024 when rounded down
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How many have an IQ between 70 and 130?
Same Procedure:
z(70) = (70-100)/15 = -2
z(130) = (130-100)/15 = 2
---
%(70<= x <= 130) = %(-2<= z <=2) = 0.9545
---
# with IQ between 70 and 130 = 0.9545*1500 = 1432 when rounded up
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How many have an IQ of 145?
Ans: zero
Why? In a normal distribution the probability of
any particular value is zero.
Why? The area over a point is zero because the base is zero.
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Cheers,
Stan H.