stats i need help asap

Question

Assume that adults have IQ scores that are normally distributed with a mean of 101.6 and a standard deviation 21.9. Find the first quartile Q,, which is the IQ score separating the bottom 25% from the top 75%. (Hint: Draw a graph.)

Answer 1

using TI calculator "invNorm" option located in "Distr"

invNorm( 0.25,101.6,21.9)= 86.8286

Answer 2

will be using standardized z =: (x - mean)/SD = (x - 101.6)/21.9, where x = IQ square

find z-score associated with 25th percentile (0.25 probability) = -0.67

plug in -0.67 into standardized z equation and solve for x for 25th percentile:

-0.67 = (x - 101.6)/21.9

21.9 * -0.67 + 101.6 = x

x = 86.927