Question

The amount of time that person shops for a birthday card can be

modelled with an exponential distribution with the average time equal
to six minutes.
a. Find the probability that a person spends more than 5 minutes?
b. What is the median time spent?

Answer 1

The probability that a person spends more than five minutes shopping for a birthday card is approximately 28.65%. The median time spent is approximately 4.1589 minutes.

Step-by-step explanation:

The question revolves around the use of the exponential distribution to model the time a person spends shopping for a birthday card, with an average time of six minutes. To solve part a, which asks for the probability that a person spends more than five minutes, we will use the exponential distribution formula:

P(X > x) = e-x/λ

Where λ = 1/μ and μ is the average time.

For an average of 6 minutes, λ = 1/6. The probability of spending more than 5 minutes is:

P(X > 5) = e-5/6 = e-5×1/6 ≈ 0.2865 or 28.65%

The median time, b, of an exponential distribution is given by:

median = ln(2)/λ

So the median time spent is:

median = ln(2) × 6 ≈ 4.1589 minutes.