Question

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 105 and a standard deviation of 14. Suppose one individual is randomly chosen. Let X = IQ of an individual.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that a randomly selected person's IQ is over 97. Round your answer to 4 decimal places.

c. 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.

d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places.

Q1:

Q3:

IQR:

Answer 1

Solution:

a. The distribution of X is:

b. Find the probability that a randomly selected person's IQ is over 97.

We have to find:

Now using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, the probability that a randomly selected person's IQ is over 97 is 0.7161

c. 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?

Answer: We have to first find the z value for area = 0.04. Using the standard normal table, we have:

Now using the z-score formula, we have:

Therefore, the highest IQ score a child can have and still receive special services is 80.50

d. Find the Inter Quartile Range (IQR) for IQ scores.