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anonymous

  • 4 years ago

Can you see if you can get an answer to this question? X is distributed normally, P(X>59.1)=0.0218 and P(X>29.2)=0.9345. Find the mean and standard deviation of the distribution to 3 s.f

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  1. dumbcow
    • 4 years ago
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    Because its P(X>a) you need to do 1-P to get correct Z-values Z1 = (59.1- m)/s Z2 = (29.2 -m)/s you will have to solve system of 2 equations using substitution

  2. anonymous
    • 4 years ago
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    Yes, but is there such thing as P(X>29.2)=-0.9345?

  3. dumbcow
    • 4 years ago
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    no, probabilities must be within 0 and 1

  4. dumbcow
    • 4 years ago
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    i get m = 42 s = 8.47

  5. anonymous
    • 4 years ago
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    that's right.. How did you get that?

  6. dumbcow
    • 4 years ago
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    by solving the system of equations you should get Z1 = 2.018 Z2 = -1.51 right

  7. anonymous
    • 4 years ago
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    Wait, how did you get Z2?

  8. dumbcow
    • 4 years ago
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    looked up 1-.9345

  9. anonymous
    • 4 years ago
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    which is 0.0655... But I don't have that value on my distribution table?

  10. dumbcow
    • 4 years ago
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    just round it to the closest one.. 0.066 if you have excel, use "Norminv" function, it will give you the z-values as well

  11. anonymous
    • 4 years ago
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    It starts at 0.5? And I can't use excel in my exam, so... how can I find the value otherwise?

  12. dumbcow
    • 4 years ago
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    it doesn't show probabilities less than 0.5 ??

  13. anonymous
    • 4 years ago
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    No, it doesn't.

  14. dumbcow
    • 4 years ago
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    ok look up .9345 and flip the sign of the z-value

  15. anonymous
    • 4 years ago
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    No

  16. anonymous
    • 4 years ago
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    It's 1.51

  17. anonymous
    • 4 years ago
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    So, it'd be -1.51?

  18. dumbcow
    • 4 years ago
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    yeah, you can do that because the distribution is symmetric

  19. anonymous
    • 4 years ago
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    Ah Ok. Thanks... So from there, what are the two equations which result?

  20. dumbcow
    • 4 years ago
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    2.018 = (59.1- m)/s -1.51 = (29.2 -m)/s solve one for s --> s = (59.1-m)/2.018 plug that into 2nd equation to find m

  21. anonymous
    • 4 years ago
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    Ok. Thanks!!!

  22. dumbcow
    • 4 years ago
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    yw

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