Question

An article suggests the uniform distribution on the interval (8.5, 21) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.

(a) What are the mean and variance of depth? (Round your variance to two decimal places.)

mean
variance

(b) What is the cdf of depth?
F(x) =

0		x < 8.5
		8.5 ≤ x < 21
1		21 ≤ x

(c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.)


What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.)


(d) What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.)


What is the probability that the observed depth is within 2 standard deviations of the mean value?

Answer 1

here for uniform distribution parameter a =8.5 and b=21

a)

mean μ=(a+b)/2 =

14.75

variance =σ2= (b-a)2/12 =13.02

b)

F(x) =(x-8.5)/(21-8.5) =(x-8.5)/12.5

c) probability that observed depth is at most 10

P(X<10)=(10-8.5)/(21-8.5)=0.12

probability that observed depth is between 10 and 15

P(10<X<15)=(15-10)/(21-8.5)=0.4

d)

probability that the observed depth is within 1 standard deviation of the mean value :

P(11.1416<X<18.3584)=(18.3584-11.1416)/(21-8.5)=0.5774

probability that the observed depth is within 2 standard deviations of the mean value =1.0000