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:

c

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.