Let X denote the amount of space occupied by an articleplaced in a 1-ft3 packing container. The pdf ofX is below.
f(x) =
| 56x6(1 − x) |     | 0< x < 1 |
| 0 | | otherwise |
(a) Graph the pdf.
Obtain the cdf of X.
| F(x) = | |      0 | x < 0 | | 0 ≤ x ≤ 1 | |      1 | x > 1 |
|
Graph the cdf of X.
(b) What is P(X ≤ 0.65) [i.e., F(0.65)]?(Round your answer to four decimal places.)
(c) Using the cdf from (a), what is P(0.25 < X≤ 0.65)? (Round your answer to four decimal places.)
What is P(0.25 ≤ X ≤ 0.65)? (Round your answer tofour decimal places.)
(d) What is the 75th percentile of the distribution? (Round youranswer to four decimal places.)
(e) Compute E(X) andσX. (Round your answers to fourdecimal places.)
(f) What is the probability that X is more than 1 standarddeviation from its mean value? (Round your answer to four decimalplaces.)
