Question

The number of ants per acre in the forest is normally distributed with mean 44,000 and standard deviation 12,359. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N( , )

b. Find the probability that a randomly selected acre in the forest has fewer than 35,896 ants.

c. Find the probability that a randomly selected acre has between 42,504 and 54,849 ants.

d. Find the first quartile. ----------------- ants (round your answer to a whole number)

Answer 1

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Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(-0.6557, TRUE)" to find the probability.

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Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(0.8778, TRUE)" & "=NORM.S.DIST(-0.1210, TRUE)" to find the probability.

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Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.25 to the left of the normal curve or use excel formula "=NORM.S.INV(0.25)" to find the z-score.

Round the value to the nearest whole number