Question

The average number of acres burned by forest and range fires in a large county is 4,200 acres per year, with a standard deviation of 900 acres. The distribution of the number of acres burned is normal. Compute the probability that more than 5,000 acres will be burned in any year. b. Determine the probability that fewer than 4,000 acres will be burned in any year. c. What is the probability that between 1,500 and 4,100 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. a. The probability that more than 5,000 acres will be burned is ___ (Round to four decimal places as needed). b. The probability that fewer than 4,000 acres will be burned is _ (Round to four decimal places as needed). c. The probability that between 1,500 and 4,100 acres will be burned is _ (Round to four decimal places as needed). d. The probability help will be needed is ___ (Round to four decimal places as needed).

          The average number of acres burned by forest and range fires in a large county is 4,200 acres per year, with a standard deviation of 900 acres. The distribution of the number of acres burned is normal.

Compute the probability that more than 5,000 acres will be burned in any year.

b. Determine the probability that fewer than 4,000 acres will be burned in any year.

c. What is the probability that between 1,500 and 4,100 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.

a. The probability that more than 5,000 acres will be burned is _____ (Round to four decimal places as needed).

b. The probability that fewer than 4,000 acres will be burned is _____ (Round to four decimal places as needed).

c. The probability that between 1,500 and 4,100 acres will be burned is _____ (Round to four decimal places as needed).

d. The probability help will be needed is _____ (Round to four decimal places as needed).

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Added by Michael R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ahmet Yavas

09/21/2022

Step 1

Step 1: To find the probability that more than 5,000 acres will be burned in any year, we use the normal distribution function with a lower boundary of 5,000, upper boundary of infinity, mean of 4,200, and standard deviation of 900. Show more…

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The average number of acres burned by forest and range fires in a large county is 4,200 acres per year, with a standard deviation of 900 acres. The distribution of the number of acres burned is normal. Compute the probability that more than 5,000 acres will be burned in any year. b. Determine the probability that fewer than 4,000 acres will be burned in any year. c. What is the probability that between 1,500 and 4,100 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. a. The probability that more than 5,000 acres will be burned is _____ (Round to four decimal places as needed). b. The probability that fewer than 4,000 acres will be burned is _____ (Round to four decimal places as needed). c. The probability that between 1,500 and 4,100 acres will be burned is _____ (Round to four decimal places as needed). d. The probability help will be needed is _____ (Round to four decimal places as needed).

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00:01 For this question, there's given a normal distribution, and the mean and the standard deviation was given in the question.

00:07 Let me just take this note.

00:09 The main value, which is denoted by mu, that is equal to 4200.

00:14 And the next one is the standard deviation.

00:18 So the standard deviation, that is denoted by sigma, which is equal to 900.

00:26 So since this is a normal distribution, i can define the random variable x, which is normally distributed, that is 4 ,200.

00:33 And 900 great so in part 8 what we have to do we have to find we have to find that the problem that more than 5 ,000 acres will be burn in any year so the probability of x is greater than 5 ,000 so what that means if i just graph the normal distribution here the mean score is here which is 4200 and here is 5 ,000 so we have to get the area of this region in order to get this area, i'm going to use the normal cdf function for the graphing calculator.

01:11 When we look at this shaded region, the lower boundary is 5 ,000, and there is no in upper boundary.

01:17 That goes to infinity, so i'm going to put very big number here.

01:21 And the mean value is 4 ,200 in the standard division, 900.

01:25 Let me just put these values on the calculator.

01:28 Just press second in distribution.

01:30 You will see on the screen there's a normal cdf.

01:33 The lower boundary here is 5 ,000 and the upper boundary, which is one, this is in 99.

01:40 And the mean value is 4 ,200 and the 900.

01:46 Great.

01:46 Let's get the result.

01:48 So the probability here, how many decimal points do we need? let me just check this one here.

01:55 So nothing is sad here.

01:57 Yeah, four decimal places.

01:58 So the answer would be 0 .18 and 17.

02:03 This is the probability for the first case.

02:06 What about for part b? the terminated problem that fewer than 4 ,000, right? and so that means we need to get the probability of x is less than this is 4 ,000.

02:22 So again, i'm going to use the normal cdf function here.

02:27 The normal cdf...

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