In the Southern Ocean food web, the krill species Euphausia superba is the most important prey...

In the Southern Ocean food web, the krill species Euphausia superba is the most important prey species for many marine predators, from seabirds to the largest whales. Body lengths of the species are normally distributed with a mean of 40 mm and a standard deviation of 12 mm. (a) What is the probability that a randomly selected krill is longer than 46 mm? (b) Describe the distribution of the mean length of a sample of four krill. (c) What is the probability that the mean length of a sample of four krill is more than 46 mm? (d) Could you estimate the probabilities from parts (a) and (c) if the lengths of krill had a skewed distribution?

Solutions

Expert Solution

Let X denotes the body length of a randomly selected species.

X ~ Normal(40, 12²)

a) The probability that a randomly selected krill is longer than 46 mm

b) Let denotes the mean length of a sample of four krill.

Now,

The probability that the mean length of a sample of four krill is more than 46 mm

d) Then, it is not possible to estimate.

orchestra answered 9 months ago

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