Mathematics, 08.04.2020 05:08 Miles1111

For a certain type of copper wire, it is knownthat, on the average, 1.5 flaws occur per millimeter. Assuming that the number of flaws is a Poisson randomvariable, what is the probability that no flaws occur ina certain portion of wire of length 5 millimeters?

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Answer from: sierrabuckner397

The probability that no flaws occur in a certain portion of wire of length 5 millimeters is 0.055%

Poisson distribution is used when there are several occurrences in a distribution. It is given by:

$f(x)=\frac{e^{-\lambda}\lambda^x}{x!} \\\\where\ \lambda=mean,x=number\ of \ occurences$

For a 5 mm wire:

E(X) = 5mm * 1.5 flaws per mm = 7.5 mm

P(X = 0) = $\frac{e^{-7.5}7.5^0}{0!}=0.055\%$

The probability that no flaws occur in a certain portion of wire of length 5 millimeters is 0.055%

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Answer from: leeorareeves299

The probability that no flaws occur in a certain portion of wire of length 5 millimeters = 1.1156 occur / millimeters

Step-by-step explanation:

Step 1:-

Given data A copper wire, it is known that, on the average, 1.5 flaws occur per millimeter.

by Poisson random variable given that λ = 1.5 flaws/millimeter

Poisson distribution $P(X= r) = \frac{e^{-\alpha } \alpha ^{r} }{r!}$

Step 2:-

The probability that no flaws occur in a certain portion of wire

$P(X= 0) = \frac{e^{-1.5 } \(1.5) ^{0} }{0!}$

On simplification we get

P(x=0) = 0.223 flaws occur / millimeters

Conclusion:-

The probability that no flaws occur in a certain portion of wire of length 5 millimeters = 5 X P(X=0) = 5X 0.223 = 1.1156 occur / millimeters

Answer from: Quest

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Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

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