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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?
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?

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amistre64
 one year ago
Best ResponseYou've already chosen the best response.1what do we have to work with? calculators or tables?

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0I don't understand how to do this. I missed a few classes. I think caculatoes

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Wait no tables I'm sorry I don't have a graphic caculators

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1well i think this is assessing your knowledge about the properties of a the normal distribution ....

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1what do you know about a normal distribution?

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0I know the formula for it and such but this question confused me because there is no standard deviation

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1do you know what a zscore is?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1what 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

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1so if the data points referenced are the same distance from the mean, then we can compare the information to determine a solution

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0My formula is z= Xn/ o The n and o are Greek letters though. The n I believe is pronounced as mew but I forgot the other words name

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1sigma is the other one

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Yes that's the name thank you it slipped my mind

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443902151868:dwthats the formula I use

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1if \[\frac{x_1\mu}{\sigma}=\frac{x_2\mu}{\sigma}\] then \[x_1\mu=\mux_2\] \[x_1+x_2=2\mu\] does x1+x2 = 2u?

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0They shouldn't considering the variables are different.

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0the 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.

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Is the five percent irrelevant and used to trick you?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.18.5 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)

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0oh okay i understand so you plug these numbers into the formula and solve it correct?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1well, 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

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443902705692:dw A=B

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1so, by using the formula \[\frac{11.58.5}{\sigma}=\frac{5.58.5}{\sigma}\] we can see if they share a common 'z' value

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1some algebra just simplifies this to 11.5+5.5 = 2(8.5) of if 8.5 is the average of the 2

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1we know B=5%, we are asked to find A if the condition holds that 11.5+5.5 = 2(8.5), then A=B

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Wait I'm a bit lost

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Don't we need to find the z value to figure out the sigma though and how did you get a 2 from this equation?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1sigma is irrelevant ... it cancels out in the process

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1do you agree that we are looking to find: \[\frac{x_1\mu}{\sigma}=\frac{x_2\mu}{\sigma}\]???

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0dw: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)

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0And to solve this problem, a Z value would be needed

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1work 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 ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1we 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

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Okay i understand now

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1since 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 ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1since they are the same distance relative to the mean, they share the same tail value

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1directionwise that is left tail is equal to right tail

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Okay I understand that

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0so 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.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1its 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

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Oh alright i understand

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1we can normalize this (hence the name normal distribution) by making the mean equal to 0 5.5 < 8.5 < 11.5 well, 8.58.5 = 0, so lets subtract 8.5 from all parts 5.58.5 < 8.58.5 < 11.58.5 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

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Okay yes i got that

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1the 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

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0the bell curve yes

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443903974936:dw

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1normalising 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?

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Oh thank god I thought I did that wrong. Wow its much simpler that it looks.

Angel_Kitty12
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much, I appreciate you helping me even if i was so confused.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1stats can be confusing, i think its the speed at which it is presented ...
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