Question

Suppose that the length of research papers is uniformly distributed from 8 to 23 pages. We survey a class in which 55 research papers were turned in to a professor. We are interested in the average length of the research papers.

σ_X = (rounded to two decimal places)

Answer 1

For uniform distribution from a to b,

Mean, = (a+b)/2

Here, a = 8 and b = 23

= (8 + 23)/2

= 15.5

Standard deviation, =

=

= 4.33

For a sample of size n = 55, according to Central Limit Theorem,

Mean of sampling distribution of mean, = = 15.5

Standard error, =

=

= 0.58