An exponential distribution is formed by the time it takes for a person to choose a birthday gift. The average time it takes for a person to choose a birthday gift is 41 minutes. Given that it has already taken 24 minutes for a person to choose a birthday gift, what is the probability that it will take more than an additional 34 minutes

43.62% probability that it will take more than an additional 34 minutes

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and the conditional probability formula.

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:

The probability of finding a value higher than x is:

Conditional probability formula:

In which

P(B|A) is the probability of event B happening, given that A happened.

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Taking more than 24 minutes.

Event B: Taking ore than 24+34 = 58 minutes.

P(A)

More than 24, use the exponential distribution.

Mean of 41, so

Intersection:

More than 24 and more than 58, the intersection is more than 58. So

Then:

43.62% probability that it will take more than an additional 34 minutes