Question

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?

Answer 1

55% probability that a randomly selected depth is between 2.25 m and 5.00 m

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d is given by the following formula.

`P(c \leq X \leq d) = (d - c)/(b - a)`

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.

This means that
`a = 2, b = 7`

What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?

`P(2.25 \leq X \leq 5) = (5 - 2.25)/(7 - 2) = 0.55`

55% probability that a randomly selected depth is between 2.25 m and 5.00 m