Find the value of n(A) if n(B) = 38, n(ANB) = 17, and n(AUB) = 59. n(A)- (Type a whole number.) W More More T V
1 answer:
Answer:
Step-by-step explanation:
In sets theory n(A) represents the number of elements in set A.This number is the cardinal number of the set A.
For n(AUB) there is an equation that relates n(A),n(B) and n(A∩B) :
n(AUB) = n(A) + n(B) - n(A∩B)
In our exercise :
n(AUB) = n(A) + n(B) - n(A∩B)
Another important equation for maths is similar to this one :
P(AUB) = P(A) + P(B) - P(A∩B)
Where ''P'' is the event probability.This equation is used in probability and statistics.
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Answer:
a)
And we can find this probability using the normal standard table or excel and we got:
b)
And we can find this probability using the complement rule and the normal standard table or excel and we got:
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".
Part a
Let X the random variable that represent the time for the step 1 and Y the time for the step 2, we define the random variable R= X+Y for the total time and the distribution for R assuming independence between X and Y is:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score 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 and we got:
Part b
And we can find this probability using the complement rule and the normal standard table or excel and we got: