Question

Suppose IQ scores are normally distributed with mean 100 and standard deviation 10. Which of the following is false?

a. A normal probability plot of IQ scores of a random sample of 1,000 people should show a straight line.
b. Roughly 68% of people have IQ scores between 90 and 110.
c. An IQ score of 80 is more unusual than an IQ score of 120.
d. An IQ score greater than 130 is highly unlikely, but not impossible.

Answer 1

93Answer:

C. An IQ score of 80 is more unusual than an IQ score of 120

is the false answer

Explanation:

Firstly we need to find the probability of the test score to be less than 90(P<90) then we will continue finding the probability of the IQ score to be between 90 and 110(90<P<110) then we find the probability of the IQ score being more than 110 (P>110).

For P<90

Firstly we compute this using a scientific calculator where we choose the stat option and enter the mean of 100 and a standard deviation of 10, so we check if we make the normal random variable(X) to be 90 the outcome or answer for that is 0.16 so now we know the probability of the IQ score to be less than 90 is 16% chances.

For 90<P<110

then we check with the same method what will be the probability for an IQ score to be between 90 and 110 for a mean of 100 and a standard deviation of 10 we again check a normal random variable(X) of 110 to see what will be the probability of P<110 which we find an answer of 0.84 which is 84% chances so now therefore the probability of an IQ score to be more than 110 is 0.

therefore this tells us an IQ score of 120 is more unusual than an IQ score of 120.