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Nickie_S

  • 3 years ago

Statistics The diameters of grapefruits in a certain orchard are normally distributed with a mean of 7.30 inches and a standard deviation of 0.80 inches. Show all work. (A) What percentage of the grapefruits in this orchard have diameters less than 6.7 inches? (B) What percentage of the grapefruits in this orchard are larger than 7.20 inches? What I have wrote out mean=m=7.30 Standard deviation=s=0.80 (A) what % have diameters less than 6.7 (B) what %are larger than 7.20

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  1. amistre64
    • 3 years ago
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    A is asking: P(X<6.7)

  2. amistre64
    • 3 years ago
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    B is asking P(X>7.2)

  3. amistre64
    • 3 years ago
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    z = (6.7 - mean)/sd

  4. Nickie_S
    • 3 years ago
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    6.7-7.30/0.80

  5. amistre64
    • 3 years ago
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    good, thats our z score for A

  6. amistre64
    • 3 years ago
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    we get a negative and we know that it wants the value of everything to the left of it

  7. amistre64
    • 3 years ago
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    .5 - zvalue

  8. amistre64
    • 3 years ago
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    zvalue will probably be called a Pvalue later in the book

  9. Nickie_S
    • 3 years ago
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    -0.75

  10. amistre64
    • 3 years ago
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    yep

  11. mathTalk
    • 3 years ago
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    Can we use the bell curve ?

  12. amistre64
    • 3 years ago
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    we are .

  13. Nickie_S
    • 3 years ago
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    yes, mathtalk that is what they are all made of (im in statistics-the book says elementary statistics- my first class of it0

  14. mathTalk
    • 3 years ago
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    somebody show how to proceed here

  15. mathTalk
    • 3 years ago
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    please

  16. Nickie_S
    • 3 years ago
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    so 0.5000-0.2734(from the table)=

  17. amistre64
    • 3 years ago
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    its alot to wrap up form previous posts ... but in a nutshell, you get a zscore and look that up in a table to get a value

  18. amistre64
    • 3 years ago
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    then work it into the question to find an answer

  19. amistre64
    • 3 years ago
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    .2734 is good, so that should do it for A

  20. amistre64
    • 3 years ago
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    B is trickier in that it wants values all to the right of z

  21. amistre64
    • 3 years ago
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    same concept, but we have to adjust our thinking a little to accomodate for it

  22. Nickie_S
    • 3 years ago
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    don't we do 0.5000-0.2734?

  23. amistre64
    • 3 years ago
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    yes

  24. amistre64
    • 3 years ago
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    A is the result of .5 - .2734

  25. Nickie_S
    • 3 years ago
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    for the first one? right.

  26. amistre64
    • 3 years ago
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    yep

  27. Nickie_S
    • 3 years ago
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    oh ok, then i have 0.2266

  28. amistre64
    • 3 years ago
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    good

  29. Nickie_S
    • 3 years ago
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    so then I write it like this right? P(x<6.7)=0.23

  30. amistre64
    • 3 years ago
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    B needs some care taken to it.|dw:1320180861380:dw|

  31. amistre64
    • 3 years ago
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    A asks for a % so we gotta rewrite .2266 as 22.66%

  32. Nickie_S
    • 3 years ago
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    *100 .2266*100=22.66%

  33. amistre64
    • 3 years ago
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    that looks good to me

  34. Nickie_S
    • 3 years ago
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    ok, on to the second one!

  35. Nickie_S
    • 3 years ago
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    are you still here?

  36. amistre64
    • 3 years ago
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    im here

  37. amistre64
    • 3 years ago
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    lets figure the z score to get started

  38. Nickie_S
    • 3 years ago
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    ok, I have been having loading problems, so I thought it was me.

  39. Nickie_S
    • 3 years ago
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    ok

  40. Nickie_S
    • 3 years ago
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    P(x>7.2)

  41. Nickie_S
    • 3 years ago
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    wait I am trying to figure it.

  42. amistre64
    • 3 years ago
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    z = (7.2-7.3)/.8 .... same process, different numbers

  43. Nickie_S
    • 3 years ago
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    x-mean/stan dev. 7.20-7.30/0.80

  44. Nickie_S
    • 3 years ago
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    -01/0.80 -0.125/0.80 -0.15625

  45. amistre64
    • 3 years ago
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    got some typos in there... but your on the right track -.1/.8 = -.125

  46. amistre64
    • 3 years ago
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    7.2 - 7.3 = -.1 -.1/.8 = -1/8 = -.125

  47. Nickie_S
    • 3 years ago
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    and then: -0.125/0.80 =-0.15625

  48. amistre64
    • 3 years ago
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    no, there is no need to divide it again by .8

  49. Nickie_S
    • 3 years ago
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    ok, i see it. ok next step.

  50. amistre64
    • 3 years ago
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    \[z=\frac{x-\bar x}{\sigma}\] \[z=\frac{7.20-7.30}{0.80}\] \[z=\frac{-0.10}{0.80}=-0.125\]

  51. amistre64
    • 3 years ago
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    id go with the z=.13 value, but a better result would be that since this is exactly in between .12 and .13 to take the average of the values as well

  52. Nickie_S
    • 3 years ago
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    lets go with -0.13

  53. amistre64
    • 3 years ago
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    lets :)

  54. Nickie_S
    • 3 years ago
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    now I go find it in the table.

  55. amistre64
    • 3 years ago
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    yep, we need the value for this z to calculate with

  56. Nickie_S
    • 3 years ago
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    0.0517

  57. amistre64
    • 3 years ago
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    thats what i got in my table as well

  58. Nickie_S
    • 3 years ago
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    so do we take 0.5000+0.0517?

  59. amistre64
    • 3 years ago
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    we do, and you understand why right?

  60. Nickie_S
    • 3 years ago
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    because it is greater, and because it is a positive number

  61. amistre64
    • 3 years ago
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    close enough, with more practice it should become better to see it :)

  62. Nickie_S
    • 3 years ago
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    lol, I'm a begginer.

  63. amistre64
    • 3 years ago
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    one way to think of it is to get the value to the left and subtract it from the total value under the curve; the total is 1

  64. amistre64
    • 3 years ago
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    1 - (value to the left of z) = (value to the right of z)

  65. Nickie_S
    • 3 years ago
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    because the problem is a greater than, so you have to add the left side of the bell with the amount that is greater than the half.

  66. amistre64
    • 3 years ago
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    yep, that is a very good way to view it. good job ;)

  67. Nickie_S
    • 3 years ago
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    well thanks for the medal! (medals).

  68. amistre64
    • 3 years ago
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    and remember its asking for %

  69. Nickie_S
    • 3 years ago
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    so we get 0.5517

  70. Nickie_S
    • 3 years ago
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    which makes it a 55.17%

  71. amistre64
    • 3 years ago
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    good

  72. Nickie_S
    • 3 years ago
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    Ok, I have 2 more questions I need help with, and as I am learning maybe i can do most of the work. So here we go to another question, if your p for it.

  73. amistre64
    • 3 years ago
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    im good for it .... :)

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