(Solved): An article suggests the uniform distribution on the interval \( (6.5,21) \) as a model for depth \ ...

An article suggests the uniform distribution on the interval \( (6.5,21) \) as a model for depth \( (\mathrm{cm}) \) 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? \[ F(x)=\left\{\begin{array}{ll} \frac{0}{14.5} & x<6.5 \\ \frac{x-6.5}{1} & 6.5 \leq x<21 \\ \hline & 21 \leq x \end{array}\right. \] (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 ecimal What is the probability that the observed depth is within 2 standard deviations of the mean value?