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Continuous Probablility Distributions

1. For the following normal distributions with parameters as specified, calculate the required probabilities:
a) &#956; &#8776; 5, &#963; = 2; calculate P( 0<x<8)

b) &#956; &#8776; 5, &#963; = 4; calculate P( 0<x<8)

c) &#956; &#8776; 3, &#963; = 2; calculate P( 0<x<8)

d) &#956; &#8776; 4, &#963; = 3; calculate P( x>1)

e) &#956; &#8776; 0, &#963; = 3; calculate P( x>1)

2. The average number of acres burned by forest and range fires in a large New Mexico county is 4,300 acres per year, with a standard deviation of 750 acres. The distribution of the number of acres burned is normal.
a. Compute the probability in any year that more than 5,000 acres will be burned.
b. Determine the probability in any year that fewer than 4,000 acres will be burned.
c. What it is the probability that between 2,500 and 4,200 acres will be burned?
d. In those years when more than 5,500 acres are burned, help is needed from eastern-region fire teams. Determine the probability help will be needed in any year.

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