Question

Assume that adults have IQ scores that are normally distributed with a mean of 97.4 and a standard deviation 24.8. Find the first quartile Upper Q 1​, which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.)
The first quartile is?
​(Type an integer or decimal rounded to one decimal place as​ needed.)

Answer 1

Given : adults have IQ scores that are normally distributed with a mean of 97.4 and a standard deviation 24.8.

To find : IQ score separating the bottom​ 25% from the top​ 75%

Solution:

Refer Z score table

Z score = -0.675  for  lower 25 % data

Z score  = ( Value - Mean )/Standard Deviation

Value = ?

Mean = 97.4

Standard Deviation = 24.8

Z score = -0.675

=> -0.675 = ( Value - 97.4)/(24.8)

=> Value = 97.4 - 16.74

=> Value = 80.66

=> Value = 80.7

80.7  is the IQ score separating the bottom​ 25% from the top​ 75%

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