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In: Statistics and Probability

An exponential distribution is formed by the time it takes for a person to choose a...

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?

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Expert Solution

Let X is the random variable denoting the time it takes for that person to choose a birthday gift.

Then by the problem we have,

, is the parameter of the distribution.

Therefore, the p.d.f. of X is given by,

,

, otherwise

and the c.d.f. of X is given by,

,

   , otherwise

Since, the average time it takes for a person to choose a birthday gift is 41 minutes, therefore, we have

i.e.

Now, given that it has already taken 24 minutes for that person to choose a birthday gift, the probability that it will take more than an additional 34 minutes i.e. total (34 + 24) = 58 minutes

= 0.4364 (rounded to 4 decimal places)

Answer: Given that it has already taken 24 minutes for that person to choose a birthday gift, the probability that it will take more than an additional 34 minutes is 0.4364.

orchestra answered 1 year ago
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