SOLUTION: A manufacturer makes chocolate bars with a mean weight
of 110 grams and a standard deviation of 2 grams. The
weights are normally distributed.
(a) What proportion of the bars is
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-> SOLUTION: A manufacturer makes chocolate bars with a mean weight
of 110 grams and a standard deviation of 2 grams. The
weights are normally distributed.
(a) What proportion of the bars is
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Question 1162961: A manufacturer makes chocolate bars with a mean weight
of 110 grams and a standard deviation of 2 grams. The
weights are normally distributed.
(a) What proportion of the bars is likely to be less in
weight than 106 grams?
(b) The manufacturer decides to make “bigger bars” with
the same standard deviation as before. It is decided
that the covers of these bigger bars will be marked
‘minimum weight 115 grams’. What mean weight will
have to be aimed if no more than one bar in 100 is to
be less than 115 grams in weight? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! to answer question A, do the following:
mean = 110
standard deviation = 2
use the following online calculator: https://homepage.divms.uiowa.edu/~mbognar/applets/normal.html
your inputs will be:
mean = 110
standard deviation = 2
x = 106
select p(X < x) and hit the return.
the calculator then tells you that the probability of getting a chocolate bar with a weight less than 106 grams is equal to .02275.
here's what it looks like:
to answer question B, do the following.
set the mean equal to 0 and the standard deviation equal to 1
set p(X < x) to .01
hit the return and the calculator tells you that the x is equal to -2.32635.
that's the z-score that will have an area to the left of it equal to .01
here's what it looks like.
use the z-score formula of z = (x - m) / s
set z = -2.32635.
set x = 115
set s = 2
the z-score formula becomes -2.32635 = (115 - m) / 2
multiply both sides of this equation by 2 to get -2.32635 * 2 = 115 - m
subtract 115 from both sides of this equation to get -2.32635 * 2 - 115 = -m
simplify to get -119.6527 = -m
multiply both sides of the equation by -1 to get:
119.6527 = m
that's your mean.
confirm by using the calculator again.
inputs will be:
mean = 119.6527
standard deviation = 2
select p(X < x)
x = 115
hit the return and the calculator tells you that p(X < x) = .01
here's what it looks like.
this means that the probability of getting a chocolate weighing less than 115 grams when the mean is 119.6527 grams and the standard deviation is 2 grams is equal to .01.
.01 is the same as 1/100.
i'll be available to answer anyquestions you might have in regard to this.
you could solve it by using the z-score table, but there's no necessity to do so unless you are told you can't use an online calculcor to solve it.
