Question 1199349: The average speed of a certain biplane is 117.9 miles/hour.
85% of these biplanes have a speed not greater than 131 miles/hour.
This is a normal distribution.
Use your graphing calculator to find the standard deviation.
Found 2 solutions by Theo, ikleyn: Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! you would use the z-score to solve this.
mean is 117.9
x = 131
z = (x-m)/s
z is the z-score
x is the maximum speed of the biplanes.
s is the standard deviation.
use the inverse norm function of your calcuolator to see that the z-score that has 85% of the area under the normal distribution curve is equal to 1.03643338.
the z-score formula becomes 1.03643338 = (131 - 117.9) / s
solve for s to get s = (131 - 117.9) / 1.03643338 = 12.63950029.
that's the standard deviation.
here's what it looks like on a graph, using the normal distribution calculator at https://davidmlane.com/hyperstat/z_table.html
first display is using the z-score.
second display is using the raw score.
the z-score uses 0 as the mean and 1 as the standard deviation.
the raw score used 117.9 as the mean and 12.63950029 as the standard deviation, only the online calculator truncates to 6 decimal digits.
that's usually enough accuracy.
Answer by ikleyn(52832) (Show Source):
You can put this solution on YOUR website! .
The average speed of a certain biplane is 117.9 miles/hour.
85% of these biplanes have a speed not greater than 131 miles/hour.
This is a normal distribution.
Use your graphing calculator to find the standard deviation.
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We will use the condition "85% of these biplanes have a speed not greater than 131 miles/hour"
to find the raw score on this specified normal curve, that corresponds to 85% of these biplanes.
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| This score, when expressed/measured as a raw score on the specified normal curve, |
| has its specific value; but when measured in terms of the standard deviation, |
| it is the same as the standard z-score of the 85% area on the standard normal curve. |
+---------------------------------------------------------------------------------------+
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/ It is the major knowledge you need to know when solving such problems. /
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So, we first determine the standard z-score on the standard normal curve, using the condition
that 85% of the area under the standard normal curve is on the left of this standard score.
So, use the invNorm function of the graphing calculator in this format
area mean SD
standard z-score = invNorm(0.85, 0, 1) = 1.036433.
Now, we know that this standard z-score of 1.036433 is the same as the raw z-score
expressed in terms of the standard deviation
1.036433 = = .
In this equation, only SD (the standard deviation) is the unknown, so we easily find it
1.036433*SD = 131-117.9 = 13.1
SD = 13.1/1.036433 = 12.6395 (rounded).
ANSWER. The standard deviation is 12.6395 miles.
Solved.
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