Assume that adults have iq scores that are normally distributed with a mean of mu equals 105 and a standard deviation sigma equals 15. find the probability that a randomly selected adult has an iq between 87 and 123.

0.7698

Step-by-step explanation:

If you call your random variable , then what you are looking for is

because you want the probability of being between 87 and 123.

We need a table with of the normal distribution. But we can only find the table with and . Because of that, first we need to  normalize our random variable:

(you can always normalize your variable following the same formula!)

now we can do something similar to our limits, to get a better expression:

And we transform our problem to a simpler one:

(see Figure 1)

From our table we can see that (this is represented in figure 2).

Remember that the whole area below the curve is exactly 1. So we can conclude that   (because 0.8849 + 0.1151 = 1). We also know the normal distribution is symmetric, then

.

FINALLY:

b. x- 48 =120

step-by-step explanation: