SOLUTION: 2. The average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with a standard deviation of 15 minutes. Assume that the commute times are normally

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Question 629305: 2. The average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with a standard deviation of 15 minutes. Assume that the commute times are normally distributed. What proportion of commutes would be:
c. between 45 and 75 minutes?
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with a standard deviation of 15 minutes. Assume that the commute times are normally distributed. What proportion of commutes would be:
c. between 45 and 75 minutes?
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z(45) = (45-60)/15 = -1
z(75) = (75-60)/15 = 1
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Prop(45 < x < 75) = P(-1< z < 1) = 0.68
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Cheers,
Stan H.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with SD =  15 minutes

Assume that the commute times are normally distributed. 

What proportion of commutes would be: between 45 and 75 minutes? 68.2%

 z+=+%2845-60%29%2F15+=+-15%2F15+=+-1  and z+=+%2875-60%29%2F15+=+15%2F15+=+1



For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set ****

two standard deviations from the mean account for about 95.4%

and three standard deviations from the mean account for about 99.7%.



Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50%  to the right