A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Angel_Kitty12

  • one year ago

Algebra 2. The Normal Distribution. PARKING: Over several years, Bertram conducted a study of how far into parking spaces people tend to park by measuring the distance from the end of a parking space to the front fender of a car parked in the space. He discovered that the distribution of the data closely approximated a normal distribution with mean 8.5 inches. He found that about 5% of cars parked more than 11.5 inches away from the end of the parking space. What percentage of cars would you expect parked less than 5.5 inches away from the end of the parking space?

  • This Question is Closed
  1. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what do we have to work with? calculators or tables?

  2. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't understand how to do this. I missed a few classes. I think caculatoes

  3. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Wait no tables I'm sorry I don't have a graphic caculators

  4. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well i think this is assessing your knowledge about the properties of a the normal distribution ....

  5. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what do you know about a normal distribution?

  6. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I know the formula for it and such but this question confused me because there is no standard deviation

  7. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you know what a zscore is?

  8. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  9. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I believe so

  10. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what is your zscore formula ... we can work with that; and also we need to know that a normal distribution is symettric about the mean ... the percentage of data higher than a zscore of say: n is going to be equal to the data less than a zscore of: -n

  11. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so if the data points referenced are the same distance from the mean, then we can compare the information to determine a solution

  12. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    My formula is z= X-n/ o The n and o are Greek letters though. The n I believe is pronounced as mew but I forgot the other words name

  13. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sigma is the other one

  14. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes that's the name thank you it slipped my mind

  15. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1443902151868:dw|thats the formula I use

  16. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if \[\frac{x_1-\mu}{\sigma}=-\frac{x_2-\mu}{\sigma}\] then \[x_1-\mu=\mu-x_2\] \[x_1+x_2=2\mu\] does x1+x2 = 2u?

  17. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    They shouldn't considering the variables are different.

  18. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what is 11.5 + 5.5?

  19. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the mean is 8.5 and there is a few other numbers thrown in there like 11.5 and 5 percent but then they ask for the last number used what would you expect less than 5.5 so the numbers that would be used is 8.5 and 5.5 obviously.

  20. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is the five percent irrelevant and used to trick you?

  21. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    8.5 is the mean of the distribution 11.5 is one of the data points 5.5 is the other 5% is relevant only if 11.5 + 5.5 = 2(8.5)

  22. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh okay i understand so you plug these numbers into the formula and solve it correct?

  23. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well, the formula is used to calculate a zscore for each data point. a normal distribution has a symmetric property; the amount of data below and above +- z is the same. so if x1 and x2 are the same distance from the mean ... then data below and above them will be equal with respect to the conditions needed

  24. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay

  25. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1443902705692:dw| A=B

  26. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so, by using the formula \[\frac{11.5-8.5}{\sigma}=-\frac{5.5-8.5}{\sigma}\] we can see if they share a common 'z' value

  27. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    some algebra just simplifies this to 11.5+5.5 = 2(8.5) of if 8.5 is the average of the 2

  28. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we know B=5%, we are asked to find A if the condition holds that 11.5+5.5 = 2(8.5), then A=B

  29. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Wait I'm a bit lost

  30. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Don't we need to find the z value to figure out the sigma though and how did you get a 2 from this equation?

  31. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sigma is irrelevant ... it cancels out in the process

  32. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you agree that we are looking to find: \[\frac{x_1-\mu}{\sigma}=-\frac{x_2-\mu}{\sigma}\]???

  33. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1443903219200:dw| This is what I got from simplifying the problem you had shown but I'm confused how you got 11.5+5.5=2(8.5)

  34. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    And to solve this problem, a Z value would be needed

  35. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    work some algebra \[\sigma \frac{x_1-\mu}{\sigma}=-\sigma\frac{x_2-\mu}{\sigma}\] \[x_1-\mu=-(x_2-\mu)\] \[x_1-\mu=-x_2+\mu\] \[x_1-\mu+\mu=-x_2+\mu+\mu\] etc ...

  36. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we dont need a proper z value, we just need to know of 11.5 is the same distance from 8.5, as 5.5 is from 8.5 z values just tell us how many standard deviations (how far from the mean) a data point is if 2 data points are the same distance, relative to the mean, they have the same z value but differ by their signs

  37. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay i understand now

  38. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since 5.5 is 3 away from the 8.5 and 11.5 is 3 away from 8.5 they both have the same z values, for whatever the standard deviation is ...

  39. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ohhhhhhh

  40. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since they are the same distance relative to the mean, they share the same tail value

  41. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    directionwise that is left tail is equal to right tail

  42. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay I understand that

  43. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so then 11.5+5.5=2(8.5) because both 11.5 and 3.5 have the same z value from 8.5 thus multiplying it twice? Okay I'm a bit lost here....sorry. I understood everything else you said though.

  44. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    its just working the math think of it this way. if the mean is the midpoint (the average) of 2 extremes, then the extremes are the same distance from the mean

  45. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh alright i understand

  46. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we can normalize this (hence the name normal distribution) by making the mean equal to 0 5.5 < 8.5 < 11.5 well, 8.5-8.5 = 0, so lets subtract 8.5 from all parts 5.5-8.5 < 8.5-8.5 < 11.5-8.5 all we have done is reposition the data to be centered at 0 instead of 8.5 -3 < 0 < 3 now it should be easier to see that -3 and 3 are the same distance from 0

  47. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay yes i got that

  48. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the rest of the solution is just knowing that the normal distribution is symmetric about the mean; it looks the same on the left as it does the right ... |dw:1443903925176:dw| one side is a mirror of the other

  49. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the bell curve yes

  50. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1443903974936:dw|

  51. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh

  52. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    normalising the data gives us the questions He discovered that the distribution of the data closely approximated a normal distribution with mean 0 inches. He found that about 5% of cars parked more than 3 inches away from the end of the parking space. What percentage of cars would you expect parked less than -3 inches away from the end of the parking space?

  53. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    5% ?

  54. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yep

  55. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh thank god I thought I did that wrong. Wow its much simpler that it looks.

  56. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :) yeah

  57. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you so much, I appreciate you helping me even if i was so confused.

  58. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    stats can be confusing, i think its the speed at which it is presented ...

  59. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    good luck

  60. Angel_Kitty12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks a lot :)

  61. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.