An article suggests the uniform distribution on the interval from 7.5 to 20 as a

Question

An article suggests the uniform distribution on the interval from 7.5 to 20 as a model for x -depth (in centimeters) of the bioturbation layer in sediment for a certain region (a) Draw the density curve for x Density 0.10 Density 0.10 0.08 0.08 0.06 0.06 0.04 0.04 0.02 0.02 8 10 12 14 161820 8 10 2 14 1618 20 Density 0.10 Density 0.10 0.08 0.08 0.06 0.06 0.04 0.04 0.02 0.02 8 10 12 14 16 18 20 10 12 14 16 18 20 (b) What is the height of the density curve? (c) What is the probability that x is at most 13? P(x s 13)- (d) What is the probability that x is between 11 and 15? P(11 sxs 15) (e) What is the probability that x is between 16 and 20? (16 x 20) = (f) Why are the two probabilities computed in parts (d) and (e) equal? O The two probabilities are equal because they begin at the same x-value O The two probabilities are equal because their midpoints are at the same x-value O The two probabilities are equal because they end at the same x-value O The two probabilities are equal because they are represented on the graph by rectangles of equal width and equal height.

Explanation / Answer

b) Height of density curve = 1/(20 - 7.5) = 1/12.5 = 0.08

c) P(X < 13) = (13 - 7.5)/(20 - 7.5) = 5.5/12.5 = 0.44

d) P(11 < X < 15) = (15 - 11)/(20 - 7.5) = 4/12.5 = 0.32

e) P(16 < X < 20) = (20 - 16)/(20 - 7.5) = 4/12.5 = 0.32

f) Option D is correct.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.