An article suggests the uniform distribution on the interval (6.5, 21) as a mode

Question

An article suggests the uniform distribution on the interval (6.5, 21) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.

(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?

Explanation / Answer

c) P(x<=10)= (21-10)/(21-6.5)=0.7586

P(15<=x<=15)=(15-10)/(21-6.5) =0.3448

mean is (21+6.5)/2=13.75 and standard deviation is sqrt( (21-6.5)2/12)=4.1858

d) P(1 std) =2*4.1858/(21-6.5)=0.57735

P(2 std)=1

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