Which line is parallel to y = 1/4x + 6
2 answers:
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Answer:
Probability that this whole shipment will be accepted is 0.7324.
Step-by-step explanation:
We are given that a company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 30 components and accept the whole batch if there are fewer than 3 defectives.
The above situation can be represented through Binomial distribution;
where, n = number of trials (samples) taken = 30 components
r = number of success = fewer than 3
p = probability of success which in our question is % rate
of defects, i.e; 6%
<em>LET X = Number of defective components</em>
So, it means X ~
Now, Probability that this whole shipment will be accepted only when there are fewer than 3 defectives = P(X < 3)
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
=
=
= 0.7324
Therefore, probability that this whole shipment will be accepted is 0.7324.
Answer: The probability that the lengths of the three segments are the side lengths of a triangle is 0.25.
Step-by-step explanation:
Consider the event "S" as "The three segments are the sides of a triangle." Remember that the probability of an event occurring is calculated according to:
By dividing the stick into three segments, the possible cases that can be obtained writing each case in parenteses and the length of each piece as a number are:
(1, 1, 10), (1, 2, 9), (1, 3, 8), (1, 4, 7), (1, 5, 6), (2, 2, 8), (2 , 3, 7), (2, 4, 6), (2, 5, 5), (3, 3, 6), (3, 4, 5), (4, 4, 4).
which corresponds to a total of 12 total cases.
The necessary condition so that a triangle can be formed is that the sum of its two minor sides is greater than the greater side, therefore the favorable cases would be:
(2, 5, 5), (3, 4, 5), (4, 4, 4)
which corresponds to a total of 3 favorable cases. Using the probability formula we obtain: