Statistics Z Score (I think) Help?

[leggoma]

Homework Statement

So my HW is

27. Assume the heights of high school basketball players are normally distributed. For boys the mean is 74 inches with a standard deviation of 4.5 inches, while girl players have a mean height of 70 inches and standard deviation 3 inches. At a mixed 2-on-2 tournament teams are formed by randomly pairing boys with girls as teammates.

a. On average, how much taller do you expect the boy to be?

b. What will be the standard deviation of the difference in teammates’ heights?

c. On what fraction of the teams would you expect the girl to be taller than the boy?

Homework Equations

Z=X-M/Std Dev (I think its relevant)

The Attempt at a Solution

I know how to do A and B. A is 74-70 and then for B you square the std devs, add them, and then take the sq root and end up getting about 5. But for Part C, I am kind of lost. Would I use a Z score chart Z=X-M/Std Dev or do I use a normalcdf or what?

Would I do normcdf(max, min, 4,5.1)? I don't see the max or min here though

 

[nate808]

I would approach this problem by first understanding the concept of normal distribution and how it applies to the heights of high school basketball players. I would then use the given mean and standard deviation for both boys and girls to calculate the expected difference in height between a boy and a girl. This can be done by subtracting the mean height of girls from the mean height of boys.

To answer part B, I would use the formula for calculating the standard deviation of the difference in height between two teammates. This can be done by multiplying the standard deviations of both boys and girls, squaring the result, and taking the square root.

For part C, I would use the normal distribution curve to determine the fraction of teams in which the girl is expected to be taller than the boy. This can be done by calculating the Z-score for the difference in height between a boy and a girl, and then using a Z-score chart or a calculator to find the corresponding probability. The Z-score can be calculated by subtracting the mean height of girls from the mean height of boys, and then dividing by the square root of the sum of the squared standard deviations of boys and girls.

Overall, I would approach this problem by understanding the underlying concepts and using appropriate formulas and tools to solve the questions.