Question

Assume that adults have IQ scores that are normally distributed with a mean of 98.4 and a standard deviation 21.2. Find the first quartile Upper Q 1​, which is the IQ score separating the bottom​ 25% from the top​ 75%.

Can you please show how you're getting from the 0.25 to the -0.6745? That's where I'm confused. Thanks!

Answer 1

µ=   98.4  
σ =    21.2  
P(X≤x) =   0.25000  
      
z value at 0.25=   -0.6745   (excel formula =NORMSINV(0.25))
z=(x-µ)/σ      
so, X=zσ+µ=   -0.6745 *21.2+98.4
first quartile = X =   84.101   (answer)
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z value at 0.25=   -0.6745   (using excel formula =NORMSINV(0.25))

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