If men's heights are normally distributed with mean 68 and standard deviation 3.1 inches, and women's heights are normally distributed with mean 65 and standard deviation 2.8 inches, if a random man and random woman are chosen, find the probability that the woman is taller than the man.

the probability that the woman is taller than the man is  0.1423

Step-by-step explanation:

Given that :

the men's heights are normally distributed with mean  68

standard deviation   = 3.1

And

the women's heights are normally distributed with mean  65

standard deviation   = 2.8

We are to find the probability that the woman is taller than the man.

For woman now:

mean   = 65

standard deviation = 2.8

= 1-P (z , 1.07)

Using z table,

= 1 - 0.8577

= 0.1423

Thus, the probability that the woman is taller than the man is  0.1423

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.