Question

Assume the adults have IQ scores that are normally distributed with a mean of 103.5 and a standard deviation 17.9. Find the first quartile Q1, 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 that,

mean = = 103.5

standard deviation = = 17.9

Using standard normal table,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.67) = 0.25

z = -0.67 Using standard normal z table,

Using z-score formula  

x= z * +

x= -0.67 *17.9+103.5

x= 91.5