The length of life (in days) of an alkaline battery has an exponential distribution with an average life of 340 days. (Round your answers to three decimal places.) (a) What is the probability that an alkaline battery will fail before 185 days? (b) What is the probability that an alkaline battery will last beyond 2 years? (Use the fact that there are 365 days in one year.)

a) 0.42 = 42%  probability that an alkaline battery will fail before 185 days

b) 0.12 = 12% probability that an alkaline battery will last beyond 2 years

Step-by-step explanation:

Exponential distribution:

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

In which is the decay parameter.

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

Which has the following solution:

In this problem, we have that:

. So

(a) What is the probability that an alkaline battery will fail before 185 days?

0.42 = 42%  probability that an alkaline battery will fail before 185 days

(b) What is the probability that an alkaline battery will last beyond 2 years? (Use the fact that there are 365 days in one year.)

2 years = 2*365 = 730 days.

Either it lasts 730 or less days, or it last more. The sum of the probabilities of these events is decimal 1. So

We want P(X > 730). So

0.12 = 12% probability that an alkaline battery will last beyond 2 years

image result for what is another name for consecutive interior angles? ​

when two lines are crossed by another line (called the transversal): the pairs of angles on one side of the transversal but inside the two lines are called consecutive interior angles. in this example, these are consecutive interior angles: d and f.

step-by-step explanation:

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