Some psychologists believe that a genius should be defined as anyone having an iq over 140. if iq scores are normally distributed with a mean of 100 and a standard deviation of 17 and if the population of the world is 6,575,000,000, how many geniuses are there in the world today

61,239,550

Step-by-step explanation:

We let the random variable X denote the IQ scores. This would imply that X is normal with a mean of 100 and standard deviation of 17. We proceed to determine the probability that an individual chosen at random from the population would be a genius, that is;

Pr( X>140)

The next step is to evaluate the z-score associated with the IQ score of 140 by standardizing the random variable X;

The area to the right of 2.3529 will be the required probability. This area from the standard normal tables is 0.009314

From a population of 6,575,000,000 the number of geniuses would be;

6,575,000,000*0.009314 = 61,239,550

61,805,000

Step-by-step explanation:

lets assume, no of geniuses = X

P(X > 140) = P(z > (140 - 100)/17)

                = P(z > 40/17) ⇒ P(z > 2.352)

1 - P(z < 2.352) = 1 - 0.9906 ⇒ 0.0094

The number of geniuses in the world today are:

0.0094 x 6,575,000,000 = 61,805,000

they charge the same amount at 20 minutes.

step-by-step explanation:

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)