Question

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 118 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X 10 of an individual. a. A school offers special services for all children in the bottom 4% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places. b. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Ql: Q3: IQR:

Answer 1

Solution:

X: IQ of an individual

μ = 118

σ = 18

a)

for bottom 4%

Z = -1.751

x = z*σ + μ

= -1.751*18 + 118

= 86.49

Answer: 86.49

b)

Q1 = 106.86

Q3 = 130.14

IQR = 23.28