What is the value of x?
1 answer:
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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:
Answer:
64.56% probability that between 17 and 25 circuits in the sample are defective.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
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:
The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
Probability that between 17 and 25 circuits in the sample are defective.
This is the pvalue of Z when X = 25 subtrated by the pvalue of Z when X = 17. So
X = 25
has a pvalue of 0.7626.
X = 17
has a pvalue of 0.1170.
0.7626 - 0.1170 = 0.6456
64.56% probability that between 17 and 25 circuits in the sample are defective.