Question

Adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall. Approximately what percent of the adult male population is taller than the average basketball player?

Answer 1

This problem involves the normal probability distribution, and in this case we're discussing a population, not a sample.

Thus,
\[\mu=70, x=79, \sigma=3\]
(all measurements in inches).

Answer 2

ok, @mathmale

Answer 3

We want to know the percentage of players who are taller than 79 inches.
This is the area to the right of 79 under the normal curve.
Suggest you draw a diagram and mark 70, 79 and 3 on it.

Suggest you now find the z-score corresponding to 79 inches.

\[z=\frac{ x-\mu}{ \sigma }\]
Know what to do next?

Answer 4

fill in the variables?

Answer 5

@mathmale

Answer 6

Yes: find the z score corresponding to 79 inches.

Next, think of what you're looking for. Do you want the area to the left of this z score or the area to the right of it?

How are you going to find either area? Which one is easier to find? Why?

Answer 7

the right?

Answer 8

Personally I'd find the area to the left of this z. Then I'd subtract that area from 1.0000. The result would be the area to the right of this z. Have you encountered this before? Please try the calculations now.

Answer 9

z=3

Answer 10

I'm just going to take your word for that, but your answer appears to be very reasonable.
Now find the area under the standard normal curve to the left of z=3. It will be well over 0.9.

Answer 11

idk

Answer 12

Have you found areas / probabilities before, given z values?

Answer 13

Do you happen to own a TI-84 Calculator? If so, do you have it at hand?

If not, do you have a table of areas under the standard normal curve?

Answer 14

You'll need one or the other, and need to know how to use the one you have. I can help with that. but need to know where you're coming from.

Answer 15

I have an app,dont know if it works
@mathmale

Answer 16

Hope it works. What is the app for? And have you used it before?

Answer 17

I have a calculator now

Answer 18

@mathmale

Answer 19

Which one do you have? Hope it's a TI.

Answer 20

Basic calculators won't do what we need to do; we'll need a TI-83 or TI-84.
Got one?

Answer 21

yes

Answer 22

Please download this document and print it out; make it as large as you can, for easier reading. http://www.stat.purdue.edu/~mccabe/ips4tab/bmtables.pdf

Answer 23

But wait.

Answer 24

How familiar are you with the DISTR functions on the TI-83 and -84? If not very, we'd better use the table that I asked you to download and print.