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. what is the probability that x is at most 16

a) Figure attached

b) For this case we want this probability:

And we can use the complement rule:

And we can use the cumulative distribution function given by:

And replacing we got:

Step-by-step explanation:

For this case we define the random variable X= depth (in centimeters) of the bioturbation layer in sediment for a certain region, and we know the distribution for X, given by:

Part a

For this case we can see the figure attached.

Part b

For this case we want this probability:

And we can use the complement rule:

And we can use the cumulative distribution function given by:

And replacing we got:

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068