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Science Forum Index » Statistics - Math Forum » Problem on Standard Normal Distribution
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| Author |
Message |
| Satish |
 Posted: Mon Mar 26, 2007 7:15 am |
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Guest
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Hi All,
I have problem on Standard Normal Distribution:
Suppose that a new car of Brand XYZ gets a mean of 7.87 miles per
gallon, normally distributed with standard deviation 0.93 mpg. John
found that 90% of XYZ's get better gas mileage than his does. What is
his car's gas mileage?
Using Excel I could the result as:
NORMINV(1-0.9,7.87,0.93) = 6.68 miles per gallon.
I request how to solve this using the Standard Normal Tables.
Also I tried as follows:
P(X>=0.90) = P(z>-7.5), Here what would be the Z value for -7.5 from
the standard normal tables?
Request you kind help in this regard.
Regards,
Satish |
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| David Winsemius |
| Posted: Mon Mar 26, 2007 9:56 am |
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Guest
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"Satish" <satish21@gmail.com> wrote in news:1174911319.191750.147600
@l77g2000hsb.googlegroups.com:
Quote: Hi All,
I have problem on Standard Normal Distribution:
Suppose that a new car of Brand XYZ gets a mean of 7.87 miles per
gallon, normally distributed with standard deviation 0.93 mpg. John
found that 90% of XYZ's get better gas mileage than his does. What is
his car's gas mileage?
Using Excel I could the result as:
NORMINV(1-0.9,7.87,0.93) = 6.68 miles per gallon.
I request how to solve this using the Standard Normal Tables.
Also I tried as follows:
P(X>=0.90)
First you want P(x>=0.1) since 90% of the cars need to be above brand
XYZ. Look up Phi(0.1) on the normal tables and call that P. You go into
the interior values of the Normal table and find the closest number to
0.1 which on the one I have is 0.103 when z=(-1.2) (from the row) plus
(-0.0 from the column so total Z=-1.28.
Then you need to transform from the probability scale where mean=0 and
std dev=1 to the gas mileage scale where mean = 7.87 and std dev=0.93.
Solve P = -1.28 = (X-mean)/std-dev = (X-7.87)/(0.93) for X.
Quote: = P(z>-7.5),
Here what would be the Z value for -7.5 from
the standard normal tables?
I haven't figured out how you went from P(x>=.9) to P(z>-7.5) |
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