Question

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?

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