Question

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) What is the probability that between 2,500 and 4,200 acres will be burned in any given
year?

(b) What number of burnt acres corresponds to the 38th percentile?​

Answer 1

Answer:

Get the z value where

z=(x-mean)/sd

so for a. z>=(5000-4300)/750=700/750 or a z > = +0.93. This is 0.1762.

for b. z < =(4000-4300)/750=-300/750 or z < = -0.4. This is 0.3446.

for c. z=(2500-4300)/750=-2.4 and z=(4200-4300)/750=-0.13

Want a probability for z between those values, 0.5447.

The probability may be obtained from the table or with a calculator.

Explanation:

plz mark me branliest plz pLz plz

Answer 2

µ = 4300 , σ = 750

A)What is the probability that between 2,500 and 4,200 acres will be burned in any given

year?

P(2500 < X < 4200)

z=2500-4300    = -2.40

         750

z=4200-4300    = -0 13333

         750

P(2500 < X < 4200) = P(-2.40 < Z < -0.13)

P(-2.40 < Z < -0.13) = P(Z < -0.13) - P(Z < -2.40)

P(-2.40 < Z < -0.13) = 0.4483 - 0.0082 = 0.4401

B)(b) What number of burnt acres corresponds to the 38th percentile?​

P(X < ?) = 0.38 ⇒ P(Z < ?) = 0.38 ⇒ Z = -0.31

X = 4300 + (-0.31)(750)

X = 4300 – 232.5

X = 4067.5