## Nickie_S 4 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

1. amistre64

2. amistre64

3. amistre64

z = (6.7 - mean)/sd

4. Nickie_S

6.7-7.30/0.80

5. amistre64

good, thats our z score for A

6. amistre64

we get a negative and we know that it wants the value of everything to the left of it

7. amistre64

.5 - zvalue

8. amistre64

zvalue will probably be called a Pvalue later in the book

9. Nickie_S

-0.75

10. amistre64

yep

11. mathTalk

Can we use the bell curve ?

12. amistre64

we are .

13. Nickie_S

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

somebody show how to proceed here

15. mathTalk

16. Nickie_S

so 0.5000-0.2734(from the table)=

17. amistre64

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

then work it into the question to find an answer

19. amistre64

.2734 is good, so that should do it for A

20. amistre64

B is trickier in that it wants values all to the right of z

21. amistre64

same concept, but we have to adjust our thinking a little to accomodate for it

22. Nickie_S

don't we do 0.5000-0.2734?

23. amistre64

yes

24. amistre64

A is the result of .5 - .2734

25. Nickie_S

for the first one? right.

26. amistre64

yep

27. Nickie_S

oh ok, then i have 0.2266

28. amistre64

good

29. Nickie_S

so then I write it like this right? P(x<6.7)=0.23

30. amistre64

B needs some care taken to it.|dw:1320180861380:dw|

31. amistre64

A asks for a % so we gotta rewrite .2266 as 22.66%

32. Nickie_S

*100 .2266*100=22.66%

33. amistre64

that looks good to me

34. Nickie_S

ok, on to the second one!

35. Nickie_S

are you still here?

36. amistre64

im here

37. amistre64

lets figure the z score to get started

38. Nickie_S

ok, I have been having loading problems, so I thought it was me.

39. Nickie_S

ok

40. Nickie_S

P(x>7.2)

41. Nickie_S

wait I am trying to figure it.

42. amistre64

z = (7.2-7.3)/.8 .... same process, different numbers

43. Nickie_S

x-mean/stan dev. 7.20-7.30/0.80

44. Nickie_S

-01/0.80 -0.125/0.80 -0.15625

45. amistre64

got some typos in there... but your on the right track -.1/.8 = -.125

46. amistre64

7.2 - 7.3 = -.1 -.1/.8 = -1/8 = -.125

47. Nickie_S

and then: -0.125/0.80 =-0.15625

48. amistre64

no, there is no need to divide it again by .8

49. Nickie_S

ok, i see it. ok next step.

50. amistre64

$z=\frac{x-\bar x}{\sigma}$ $z=\frac{7.20-7.30}{0.80}$ $z=\frac{-0.10}{0.80}=-0.125$

51. amistre64

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

lets go with -0.13

53. amistre64

lets :)

54. Nickie_S

now I go find it in the table.

55. amistre64

yep, we need the value for this z to calculate with

56. Nickie_S

0.0517

57. amistre64

thats what i got in my table as well

58. Nickie_S

so do we take 0.5000+0.0517?

59. amistre64

we do, and you understand why right?

60. Nickie_S

because it is greater, and because it is a positive number

61. amistre64

close enough, with more practice it should become better to see it :)

62. Nickie_S

lol, I'm a begginer.

63. amistre64

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

1 - (value to the left of z) = (value to the right of z)

65. Nickie_S

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

yep, that is a very good way to view it. good job ;)

67. Nickie_S

well thanks for the medal! (medals).

68. amistre64

and remember its asking for %

69. Nickie_S

so we get 0.5517

70. Nickie_S

which makes it a 55.17%

71. amistre64

good

72. Nickie_S

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

im good for it .... :)