Question

An article suggests the uniform distribution on the interval (8.5, 19) 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 < 191 = 19 ? 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

Answer:

Step-by-step explanation:

Given that  the uniform distribution on the interval (8.5, 19) as a model for depth (cm) of the bioturbation layer in sediment in a certain region

a) Mean =$\frac{1}{19-8.5} =13.75$

b) Variance = $\frac{19^2-8.5^2}{12} \\=24.0625$=24.06

c) the probability that observed depth is at most 10=$\frac{10-8.5}{19-8.5} =0.1429$

d) the probability that observed depth is between 10 and 15=

$\frac{15-10}{19-8.5} =0.4762$

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

=P(13.75-4.9053<x<13.75+4.9053)

=P(8.8447<x<18.7553)

= P(8.84<x<18.76)

$\frac{9.92}{10.5} \\=0.945$

f) 2 std deviation will cover full interval

So prob =1