Question

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find Upper P 40​, which is the IQ score separating the bottom 40​% from the top 60​%. Round your answer to nearest tenth.

Answer 1

Answer:

$z=-0.253$

And if we solve for a we got

$a=100 -0.253*15=96.205$

And for this case the value would be 96.2 for the P40

Step-by-step explanation:

Let X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(100,15)$  

Where $\mu=100$ and $\sigma=15$

We want to find the P40 ( a) so we need to satisfy the following condition:

$P(X>a)=0.60$   (a)

$P(X$   (b)

For this case we can look for the critical value in the normal standar ddistirbution who accumulate 0.4 of the area in the left and 0.6 in the right and we got z=-0.253.

If we use condition (b) from previous we have this:

$P(X$  

$P(z$

And we can set up the following equationL

$z=-0.253$

And if we solve for a we got

$a=100 -0.253*15=96.205$

And for this case the value would be 96.2 for the P40