plz help: in a study of 82 video game players, the researchers found that the ages of these players were normally distributed, with a mean of 17 years and a standard deviation of 3 years. determine if there were 15 video game players in this study over the age of 20. justify your answer

Question

anonymous · Answer

@mathmale

mathmale · Answer

Hello, Lyubas!  In what way could I help you with this problem?
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mathmale · Answer

Are you familiar with any of these?
1) z-scores
2) Empirical Rule
3) Normal distribution

anonymous · Answer

hey  yes I am

anonymous · Answer

@mathmale

mathmale · Answer

@lyubas, what is the z score of 20, which is 1 std. dev. above the mean (17)?

mathmale · Answer

An alternative question:  Please evaluate this:$$z=\frac{ 20-17 }{ 3 }$$

mathmale · Answer

...noting that 17 is the mean, and that 3 is the std. dev.

anonymous · Answer

I understand this what do we do once u solve it

anonymous · Answer

and how did u no to use zscore in this problem? @mathmale

anonymous · Answer

I got z=1

mathmale · Answer

that's correct, lyubas.  Now if you have a table of z scores (normal probability), could you find the area under the probability curve from the extreme left up to z=1?  In other words, just look at the table, find z=+1, and write down the decimal that goes with that z-score.  What is this probability?  It's the area under the curve.  

You could also obtain this result using a TI-83 or -84 calculator.  Let me know if you need instructions for doing that.

anonymous · Answer

u do cdf on ur cal?

anonymous · Answer

@mathslover plz help

mathmale · Answer

sorry...OpenStudy has been so overused tonight that I log out, do something else and then return.

Yes, you can use the cumulative density function (CDF) to find the area under the standard normal curve to the left of z=1.  Here's the key sequence:

2nd DISTR   2 (for normalcdf(     )    -100, 1 )
Just before you press the enter key, you should see the following on your display:

normalcdf(-100,1)

Press enter.  result:  0.8413.

mathmale · Answer

This tells us that 84.13% of your 82 players are under 20 years old.

You have 82 players, lyubas.  Please multiply that 82 by 0.8413.  What do you get?

That number, rounded off, represents the number of those 82 players who are under 20.

To answer this question, subtract that number from 82.  The result is the number of players who are older than 20.  

can you now answer the original question?