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Nickie_S

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

  • 2 years ago
  • 2 years ago

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  1. amistre64
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    A is asking: P(X<6.7)

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

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

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

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

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

    • 2 years ago
  7. amistre64
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    .5 - zvalue

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

    • 2 years ago
  9. Nickie_S
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    -0.75

    • 2 years ago
  10. amistre64
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    yep

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

    • 2 years ago
  12. amistre64
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    we are .

    • 2 years ago
  13. Nickie_S
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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

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

    • 2 years ago
  15. mathTalk
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    please

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

    • 2 years ago
  17. amistre64
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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

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

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

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

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

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

    • 2 years ago
  23. amistre64
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    yes

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

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

    • 2 years ago
  26. amistre64
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    yep

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

    • 2 years ago
  28. amistre64
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    good

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

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

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

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

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

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

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

    • 2 years ago
  36. amistre64
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    im here

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

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

    • 2 years ago
  39. Nickie_S
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    ok

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

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

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

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

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

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

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

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

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

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

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

    • 2 years ago
  51. amistre64
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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

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

    • 2 years ago
  53. amistre64
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    lets :)

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

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

    • 2 years ago
  56. Nickie_S
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    0.0517

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

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

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

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

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

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

    • 2 years ago
  63. amistre64
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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

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

    • 2 years ago
  65. Nickie_S
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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.

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

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

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

    • 2 years ago
  69. Nickie_S
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    so we get 0.5517

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

    • 2 years ago
  71. amistre64
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    good

    • 2 years ago
  72. Nickie_S
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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.

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

    • 2 years ago
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