Question

Assume that adults have IQ scores that are normally distributed with a mean of 95.7 and a standard deviation 21.7. Find the first quartile Upper Q 1, which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.)

Answer 1

Given that, mean (μ) = 95.7 and standard deviation = 21.7

Let X ~ N(95.7, 21.7)

We want to find, the value of x such that, P(X ≤ x) = 0.25

Therefore, the first quartile Q1 is 81.16

Note : Using standard normal z-table we get, z-score corresponding probability of 0.25 is, z = -0.67

That is, Z0.25 = -0.67

If we used Excel then, we get z = -0.67449 and hence we get required value of first quartile Q1 = 81.06