A survey of 250 lobster fishermen found that they catch an average of 32 pounds of lobster per day with a standard deviation of four pounds. if a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?

Question

Mathematics

Darren Sosa

15 February, 16:59

A survey of 250 lobster fishermen found that they catch an average of 32 pounds of lobster per day with a standard deviation of four pounds. if a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?

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Opie · Answer 1

The P (X<31.5) will be found as follows:

z = (x-μ) / σ

thus the z-score will be:

z = (31.5-32) / 4

z=-0.125

Thus

P (x<31.5) = P (z=-0.125) = 0.4522

Answer P (x<31.5) = 0.4522