Question

• The student will examine properties of the Central Limit Theorem for averages. Use correct units where appropriate (inches, years, etc). The axes of graphs should be drawn

with a ruler or computer. Work will be graded for neatness, completeness and correctness.
The lifetime of a certain kind of battery is exponentially distributed, with an average lifetime of 20 hours.

1. We are interested in the lifetime of one battery. Define the random variable X in words.

2. Give the distribution of X using numbers, letters and symbols as appropriate. X~_______________

3. Find the probability that the lifetime of one battery is between 20 and 25 hours.

4. Draw a graph to represent the probability in #3. Shade an appropriate region.

Answer 1

In order to solve this question I used R software.

R codes and output:

> pexp(25,1/20) - pexp(20,1/20)
[1] 0.08137464
> x=seq(0,30)
> px=dexp(x,1/20)
> plot(x,px,type='l')
> abline(v=c(20,25))

Que.1

Random variable X is the lifetime of a battery.

Que.2

Where is the mean.

Que.3

P ( 20 < X < 25 ) = P ( X< 25 ) - P( X < 20 ) = 0.0814

Que.4