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Makovka662 [10]
3 years ago
8

The​ life, in​ years, of a certain type of electrical switch has an exponential distribution with an average life β=44. If 100 o

f these switches are installed in different​ systems, what is the probability that at most 15 fail during the first​ year?
Mathematics
1 answer:
Bond [772]3 years ago
3 0

Answer:

0.9999

Step-by-step explanation:

Let X be the random variable that measures the time that a switch will survive.

If X has an exponential distribution with an average life β=44, then the probability that a switch will survive less than n years is given by

\bf P(X

So, the probability that a switch fails in the first year is

\bf P(X

Now we have 100 of these switches installed in different systems, and let Y be the random variable that measures the the probability that exactly k switches will fail in the first year.

Y can be modeled with a binomial distribution where the probability of “success” (failure of a switch) equals 0.0225 and  

\bf P(Y=k)=\binom{100}{k}(0.02247)^k(1-0.02247)^{100-k}

where  

\bf \binom{100}{k} equals combinations of 100 taken k at a time.

The probability that at most 15 fail during the first year is

\bf \sum_{k=0}^{15}\binom{100}{k}(0.02247)^k(1-0.02247)^{100-k}=0.9999

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Answer:

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Step-by-step explanation:

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Elis [28]

That is a question about perimeter of rectangle.

The perimeter of a geometric shape is the sum of the value of the all sides.

In a rectangle, the opposite sides are cogruentes (equals). For example, look at picture below. In that rectangle, the sides AB and DC are equals, and the sides AD and BC are equals.

So, the sides of that rectangular table are: 1.52m, 1.52m, 0.75m and 0.75.

Therefore, the perimeter of that rectangle is 1.52+1.52+0.75+0.75= 4.54m.

But that is not the final answer because that is the perimeter in meters and the question want the answer in centimeters.

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The dimensions of a rectangular flower bed on a sketch are 4 cm by 6 cm. In real life, the shorter side of the flower bed is 5 m
Fittoniya [83]

Answer:

The correct answer is 7.5

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