SOLUTION: I am working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. I need to determine the value of x from the following information:
a
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a
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Question 274080: I am working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. I need to determine the value of x from the following information:
a) 60% fo the values are greater than x
b) x is less than 17% of the values
c) 22% of the values are less than x
d) x is greater than 55% of the values. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! I am working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. I need to determine the value of x from the following information:
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Please draw a picture of the normal curve so you can see what
these problems are asking you to find.
Put 200 at the middle mark and note that sigma = 47.
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a) 60% of the values are greater than x
So you want a right tail that has 60% of the area in it.
1st: Find the z-value that marks off that region:
invNorm(0.4) = -0.2533
2nd: Find the corresponding "x" value using
x = z*sigma + u
x = -0.2533*47 + 200
x = 188.09
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b) x is less than 17% of the values
Right-tail has 17% of the area
z value = invNorm(0.83) = 0.9542
x value = 0.9542*47+200 = 244.85
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c) 22% of the values are less than x
Left-tail of 22%
z-value = invNorm(0.22) = -0.7722
x-value = -0.7722*47+200 = 163.71
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d) x is greater than 55% of the values
Left-tail of 55%
z-value = invNorm(0.55) = 0.1257
x-value = 0.1257*47+200 = 205.91
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Cheers,
Stan H.
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