The number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,394. 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( 42000 12394 b. Find the probability that a randomly selected acre in the forest has fewer than 32,435 ants. c. Find the probability that a randomly selected acre has between 43,906 and 55,973 ants. d. Find the first quartile. ants (round your answer to a whole number)

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Please answer B, C, & D 

The problem addresses the distribution of ants per acre in a forest.

Given:
- The number of ants per acre is normally distributed with a mean (\(\mu\)) of 42,000 and a standard deviation (\(\sigma\)) of 12,394.
- Let \(X\) represent the number of ants in a randomly selected acre.

Tasks:
a. **Distribution of X**: \(X \sim N(42000, 12394)\)

b. **Probability Calculation**: Find the probability that a randomly selected acre has fewer than 32,435 ants. (Answer not provided in image)

c. **Probability Calculation**: Find the probability that a randomly selected acre has between 43,906 and 55,973 ants. (Answer not provided in image)

d. **First Quartile**: Calculate the first quartile, rounding the answer to a whole number. (Answer not provided in image)

The tasks involve calculating probabilities and quartiles based on the normal distribution parameters provided.
Transcribed Image Text:The problem addresses the distribution of ants per acre in a forest. Given: - The number of ants per acre is normally distributed with a mean (\(\mu\)) of 42,000 and a standard deviation (\(\sigma\)) of 12,394. - Let \(X\) represent the number of ants in a randomly selected acre. Tasks: a. **Distribution of X**: \(X \sim N(42000, 12394)\) b. **Probability Calculation**: Find the probability that a randomly selected acre has fewer than 32,435 ants. (Answer not provided in image) c. **Probability Calculation**: Find the probability that a randomly selected acre has between 43,906 and 55,973 ants. (Answer not provided in image) d. **First Quartile**: Calculate the first quartile, rounding the answer to a whole number. (Answer not provided in image) The tasks involve calculating probabilities and quartiles based on the normal distribution parameters provided.
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