Astudent uses pens whose lifetime is an exponential random variable with mean 1 week. use the central limit theorem to determine the minimum number of pens he should buy at the beginning of a 15-week semester, so that with probability .99 he does not run out of pens during the semester.

Student needs pens= n = 27.04

Rounding off with upper floor function ⇒ n =28

Rounding off with lower floor function ⇒ n =27

Step-by-step explanation:

Given that lifetime of each pen is a exponential random variable with mean 1 week.

Let be total sum of lifetime of n pens.

So mean of = μ = n.1

Standard deviation of =

Probability that he doesnot run out of pens= 0.99

Considering Sn be sum of n lifetimes, using central limit theorem

From table of standard normal distribution

Solving the quadratic Equation in variable x we get

n=27.04