The number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,479. 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 ~ Nb. Find the probability that a randomly selected acre in the forest has fewer than 34,078 ants.c. Find the probability that a randomly selected acre has between 35,392 and 42,240 ants. d. Find the first quartile.

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Asked Feb 6, 2020
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The number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,479. 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 34,078 ants.

c. Find the probability that a randomly selected acre has between 35,392 and 42,240 ants. 

d. Find the first quartile.

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Expert Answer

Step 1

a.

The distribution of X,

Statistics homework question answer, step 1, image 1

 

Step 2

b.

The probability that a randomly selected acre in the forest has fewer than 34,078 ants is,

Statistics homework question answer, step 2, image 1

Thus, the probability that a randomly selected acre in the forest has fewer than 34,078 ants is 0.2627.

Step 3

c.

The probability that a randomly selected acre in the forest has between 35,392 and 42,240 ants is,

Statistics homework question answer, step 3, image 1

Thus, the probability that a randomly selected acre in the forest has between 35,392 and 42,240 ants is 0.6932.

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