The length of life of an electronic component has an exponential probability density function with mean 1000 hours. Find the pro
1 answer:
The probability that a component lasts at least 1500 hours using the exponential probability density function is <u>0.22313016014843</u>.
The formula used to define the exponential distribution is called the exponential distribution formula. The variable needs to be continuous and independent for an exponential distribution. You may find the exponential distribution formula by using:
Where m is the rate parameter or the decay parameter, and μ is the mean.
In the question, the mean, μ = 1000 hours, and the variable, x = 1500 hours.
But, we need to find the probability that the component lasts at least 1500 hours, that is, x is greater than or equal to 1500, that is, f(x ≥ 1500), which, using the calculator, is computed to be <u>0.22313016014843</u>.
Thus, the probability that a component lasts at least 1500 hours using the exponential probability density function is <u>0.22313016014843</u>.
Learn more about the exponential probability density function at
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Answer:
Step-by-step explanation:
hope this helps :)
To model this situation, we are going to use the exponential function: 
where
is the initial number of cars
is the growing rate in decimal form
is number of tames the growing rate is increasing per year
is the time in years
To convert the growing rate to decimal form, we are going to divide the rate by 100%
Since the growing rate is increasing quarterly,
. We also know that the initial number of cars is 920, so 
. Lets replace all those values in our function:
We can conclude that:
Rate ---------> The quarterly rate of growth is 0.03 or 3%
Exponent --------> The compound periods multiplied by the number of years is 4t
Coefficient--------> The initial number of cars serviced is 920
Base------> The growth factor is represented by 1.03
where
To convert the growing rate to decimal form, we are going to divide the rate by 100%
Since the growing rate is increasing quarterly,
We can conclude that:
Rate ---------> The quarterly rate of growth is 0.03 or 3%
Exponent --------> The compound periods multiplied by the number of years is 4t
Coefficient--------> The initial number of cars serviced is 920
Base------> The growth factor is represented by 1.03