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2 answers:
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The table in the attached figure
<span>Pennies made before 1983
</span>Part a) find the mean
we have
[3.1047,3.1082, 3.1582, 3.0776, 3.1276, 3.1035]
Mean 1=[3.1047+3.1082 + 3.1582 + 3.0776 + 3.1276 + 3.1035]/6
Mean 1=3.1133 grams
the answer part a) is
The mean weight of the pennies made before 1983 is 3.1133 grams.
Part b)
to find the Median, place the numbers in value order and find the middle.
[3.1047,3.1082, 3.1582, 3.0776, 3.1276, 3.1035]
[3.0776, 3.1035, 3.1047,3.1082, 3.1276, 3.1582]
(3.1047+3.1082)/2=3.10645 grams
the answer part b) is
The median weight of the pennies made before 1983 is 3.10645 grams.
<span>Pennies made after 1983
</span>Part c) find the mean
we have
[2.4842, 2.4828, 2.5024, 2.4997, 2.4907, 2.4956]
Mean 2=[2.4842 + 2.4828 + 2.5024 + 2.4997 + 2.4907 + 2.4956]/6
Mean 2=2.4926 grams
the answer part c) is
The mean weight of the pennies made after 1983 is 2.4926 grams.
Part d)
to find the Median, place the numbers in value order and find the middle
[2.4842, 2.4828, 2.5024, 2.4997, 2.4907, 2.4956]
[2.4828, 2.4842, 2.4907, 2.4956, 2.4997, 2.5024]
[2.4907 +2.4956]/2=2.49315
the answer part d) is
The median weight of the pennies made after 1983 is 2.49315<span> grams.
</span>
Part e) compare the means
<span>Find the percentage difference
</span> the percentage difference is the difference between the new value and the old value, divided by the old value
so
new value=2.4926 grams
old value=3.1133 grams
[3.1133-2.4926]/3.1133------> 0.20-----> 20%
that means
<span>the difference in the means is considerable to be greater than 5%</span>
<span>Pennies made before 1983
</span>Part a) find the mean
we have
[3.1047,3.1082, 3.1582, 3.0776, 3.1276, 3.1035]
Mean 1=[3.1047+3.1082 + 3.1582 + 3.0776 + 3.1276 + 3.1035]/6
Mean 1=3.1133 grams
the answer part a) is
The mean weight of the pennies made before 1983 is 3.1133 grams.
Part b)
to find the Median, place the numbers in value order and find the middle.
[3.1047,3.1082, 3.1582, 3.0776, 3.1276, 3.1035]
[3.0776, 3.1035, 3.1047,3.1082, 3.1276, 3.1582]
(3.1047+3.1082)/2=3.10645 grams
the answer part b) is
The median weight of the pennies made before 1983 is 3.10645 grams.
<span>Pennies made after 1983
</span>Part c) find the mean
we have
[2.4842, 2.4828, 2.5024, 2.4997, 2.4907, 2.4956]
Mean 2=[2.4842 + 2.4828 + 2.5024 + 2.4997 + 2.4907 + 2.4956]/6
Mean 2=2.4926 grams
the answer part c) is
The mean weight of the pennies made after 1983 is 2.4926 grams.
Part d)
to find the Median, place the numbers in value order and find the middle
[2.4842, 2.4828, 2.5024, 2.4997, 2.4907, 2.4956]
[2.4828, 2.4842, 2.4907, 2.4956, 2.4997, 2.5024]
[2.4907 +2.4956]/2=2.49315
the answer part d) is
The median weight of the pennies made after 1983 is 2.49315<span> grams.
</span>
Part e) compare the means
<span>Find the percentage difference
</span> the percentage difference is the difference between the new value and the old value, divided by the old value
so
new value=2.4926 grams
old value=3.1133 grams
[3.1133-2.4926]/3.1133------> 0.20-----> 20%
that means
<span>the difference in the means is considerable to be greater than 5%</span>
Answer:
a) We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.
b) There is a 15.97% probability that x will be between 54 and 55.
c) The 47th percentile of x is .
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11.
This means that .
We have to find the standard deviation of the sample, that is:
(a) Is it appropriate to use the normal distribution to find probabilities for x?
We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.
(b) Find the probability that x will be between 54 and 55.
This is the pvalue of the Z score when X = 55 subtracted by the pvalue of the Z score when X = 54.
X = 55
has a pvalue of 0.88877.
X = 54
has a pvalue of 0.72907.
So, there is a 0.88877 - 0.72907 = 0.1597 = 15.97% probability that x will be between 54 and 55.
(c) Find the 47th percentile of x. Round the answer to at least two decimal places.
This is the value of X when Z has a pvalue of 0.47;
This is between and
. So we use
.
The 47th percentile of x is .