SOLUTION: A box of cookies contains a mean mass of 180g with and standard deviation of 2g.
A.) one box had a mass that corresponds to a z-score of -1.5. How many grams of cookies did this
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-> SOLUTION: A box of cookies contains a mean mass of 180g with and standard deviation of 2g.
A.) one box had a mass that corresponds to a z-score of -1.5. How many grams of cookies did this
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Question 205565: A box of cookies contains a mean mass of 180g with and standard deviation of 2g.
A.) one box had a mass that corresponds to a z-score of -1.5. How many grams of cookies did this box contain.
B.)If the mean mass of these boxes is assumed to be normal distributed, what is the probabilty a box of cookies will contain less the 179g? Found 2 solutions by stanbon, Theo:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! --------------------------------------------------------------------
A box of cookies contains a mean mass of 180g with and standard deviation of 2g.
A.) one box had a mass that corresponds to a z-score of -1.5. How many grams of cookies did this box contain.
Use x = z*sigma + u
Your Problem:
x = -1.5*2 + 180
x = -3 + 180
x = 177 g
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B.)If the mean mass of these boxes is assumed to be normal distributed, what is the probabilty a box of cookies will contain less the 179g?
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Find the z-score of 179
z(179) = (179-180)/2 = -1/2
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P(x<179) = P(z<-1/2) = 0.3085
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Cheers,
Stan H.
You can put this solution on YOUR website! A box of cookies contains a mean mass of 180g with and standard deviation of 2g.
A.) one box had a mass that corresponds to a z-score of -1.5. How many grams of cookies did this box contain.
B.)If the mean mass of these boxes is assumed to be normal distributed, what is the probabilty a box of cookies will contain less the 179g?
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mean is 180 grams and standard deviation is 2 grams.
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A.) one box had a mass that corresponds to a z-score of -1.5. How many grams of cookies did this box contain.
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a z score of -1.5 means that the box of cookies is 1.5 times the standard deviation below the mean. since the standard deviation is 2 grams than 1.5 times the standard deviations is 1.5 * 2 = 3 grams.
A box of cookies that is - 1.5 standard deviations from the mean would be - 3 grams from the mean which means that the box of cookies is 177 grams.
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B.)If the mean mass of these boxes is assumed to be normally distributed, what is the probabilty a box of cookies will contain less then 179g?
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The probability of a box of cookies being less than 179 grams is the area under the normal distribution curve to the left of 179 grams.
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looking at an online z table calculator, this was determined to be:
.308538 which means that the probability of the box of cookies being less than 179 grams is .308538.
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The online calculator can be found at the following website address:
http://davidmlane.com/hyperstat/z_table.html
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a picture of the results can be found at the following website address:
http://theo.x10hosting.com/
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if it's not there right away, it will be within a half hour.
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you enter the mean which is 180.
you enter the standard deviation which is 2.
your enter 179 in the below box and the answer will be shown at the bottom of all the selection boxes.
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without the z table calculator you would have to look the answer up in a z table. these provide the same answer, only manually.
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to convert from raw score to z score you do the following:
(R-M)/S = Z
R = raw score
M = mean
S = standard deviation
Z = Z score
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Example:
R = 177
M = 180
S = 2
Z = (177 - 180) / 2 = -3 / 2 = -1.5
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converting from Z to R is the reverse.
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formula is:
R = Z*S + M
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Example:
Z = -1.5
M = 180
S = 2
R = (-1.5)*2 + 180 = -3 + 180 = 177
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