Alice took out a loan for $19,500 at 13 1/2% on march 4, 2015 which will be due on january 14, 2016. using ordinary interest, what will be the interest cost and what amount will alice pay back on january 14, 2016

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Ответ:

ellaemtagedeane

29.08.2021

Mathematics

0.4866 = 48.66% probability that the engine will fail before it is inspected

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Exponentially distributed with mean 900 hours.

This means that $m = 900, \mu = \frac{1}{900}$

If the engine is inspected every 600 hours of flight time, what is the probability that the engine will fail before it is inspected?

This is $P(X \leq 600)$ , which is:

$P(X \leq 600) = 1 - e^{-\frac{600}{900}} = 0.4866$

0.4866 = 48.66% probability that the engine will fail before it is inspected

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