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Statistics homework problem??I need some help on this one, please!!

 
 
Reply Mon 12 Mar, 2012 09:08 pm
13. Ratings on the electric car by owners of Leaf are normally distributed with a mean of 5 and a standard deviation of 1

a. Find the percent of Leaf owners who rate the car between 2.5 and 7.5.

b. If 200 Leaf owners are queried, how many are expected to rate their car

1) Between 4 and 6?

2) Less than or equal 3?

3) Greater than equal 7?
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engineer
 
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Reply Mon 12 Mar, 2012 11:54 pm
@mihanni21 ,
For each question you need to determine the z score. The formula is

z = (x - mean)/standard deviation

They've made it easy for you by making the SD=1. Once you have the z score, look up the cummulative distribution for that z score in a cum prob table (or use the function NORMDIST in Excel and just enter the value of x, the mean, the standard deviation and then TRUE for cummulative.)

Use this approach over and over. As an example, for the first one, find the cum prob for 7.5 and substract the cum prob for 2.5. In part b, multiply the probabilities by 200 to get the number of expected users.
mihanni21
 
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Reply Tue 13 Mar, 2012 10:42 am
@engineer,
so for part a) it would be 7.5-2.5=5
z=x-mean divided by standard deviation, that would be 5-5/1= 0?? seems like I did something wrong still??
raprap
 
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Reply Tue 13 Mar, 2012 11:50 am
@mihanni21 ,
You aren't using the standard normal distribution

x is variable
mean is mu (average)
sigma is standard deviation

Z (2.5)=((2.5-5)/1)=-2.5
Z(7.5)=((7.5-5)/1)=2.5

Now use the Standard normal distribution and look up the values corresponding to these two Z values.

The first will be the value (fraction of total population) of those who rated is less than 2.5 and the second is value (same fraction) those who rated it less than 7.5.

The difference is the value (fraction of population) in the desired range.

Rap
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