Answer:
D. 37.947
Step-by-step explanation:
Heron's formula makes use of the value "s", the semi-perimeter. Here, ...
s = (7 + 11 + 12)/2 = 15
Then the area is ...
A = √(s(s -a)(s -b)(s -c)) = √(15·3·4·8) = √1440 = 12√10 ≈ 37.947
_____
<em>Comment on answer choices</em>
This value is verified by a triangle solver. We suspect a typographical error in the answer choices, specifically, selection D.
Answer:
DIRECT WAY EXCEL
"=NORM.DIST(75,80,3,TRUE)"
And we got:
OTHER WAY
And we can find this probability using the normal standard table or excel:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the diameter of a population, and for this case we know the distribution for X is given by:
Where and
And we know that if the diameter is 75 or less the ring would be considered defective , so then in order to find the proportion of defective we need to find the following probability:
One way to do this in excel is with the following formula:
"=NORM.DIST(75,80,3,TRUE)"
And we got:
And the other way is use the z score formula given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel: