In an extensive area of the Amazon region, fires occur with some regularity. An environmental entityconducted a study to evaluate the impact of these fires. In particular, one of the objectives of thestudy was to analyze the area affected by a fire. From a historical record with satellite images of thearea of interest, it was possible to estimate that the area burned in a fire, in hectares, can berepresented by a random variable with a Uniform distribution in the interval [2.5, 15].Based on the previous description, solve the following questions:a. Calculate the probability that the area burned in a fire is between 7.1 and 11.3 hectares.b. What is the expected value of the area burned in a fire? Interpret the result.

A random variable x is defined to have a Uniform distribution denoted by x∼U(θ1,θ2), if its…

Answered: In an extensive area of the Amazon…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. She randomly selected 54 men and 70 women to participate in the study. Each subject was required to step up and down a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained. Two sample T for Men vs Women N Mean StDev SE Mean Men Women 98% CI for mu Men - mu Women (- 12.20, - 1.00) T-Test mu Men = mu Women (vs H2 O C. Ho: H1 = H2; Ha: H1 #H2 (b) Identify the P-value and state the researcher's conclusion if the level of significance was a = 0.01. What is the P-value? P-value =
One sample has n=7 and SS=35 and a second sample has n =17 and SS =45. What is the pooled variance for these two samples?
Let x be a random variable that represents the pH of CVS brand water. The mean of this x distribution is µ = 6.5 pH. A new company wants to sell its water at CVS locations. However, CVS management believes that the new brand will have a mean pH less than the CVS brand water. A random sample of 50 water samples were taken from this new company's water and it was found that the sample mean was 6.3 pH and the sample standard deviation was s = 0.5 pH. Do the data indicate that the new company's water has a mean pH level less than 6.5, which is the pH of the CVS brand water. Use a 5% significance level. Identify the following in your answer. 1. Identify the null Ho and alternative hypotheses H1 for the problem. 2. Identify the following: Sample statistic • Test Statistic (t): (Round to three decimal places) p - value: (Round to four places) • Calculator key used. 3. Identify the significance level and determine if you reject or fail to reject the null hypothesis. 4. State your conclusion.
Water availability is of prime importance in the life cycle of most reptiles. To determine the rate of evaporative water loss of a certain species of lizard at a particular desert site, 34 such lizards were randomly collected, weighed and placed under the appropriate experimental conditions. After 24 hours, each lizard was removed, weighed, and its total water loss was calculated by subtracting its body weight after treatment from its initial body weight. Previous studies have shown that the relative frequency distribution of water loss for this species of lizard has a mean of 3.1 grams and a s.d. of 0.8 gram. a) What is the approximate sampling distribution of x , the mean water loss of the 34 lizards
In a study comparing banks in two countries, a sample of 142 matched pairs of banks was formed. Each pair contained one bank from country x and one from country y. The pairings were made in such a way that the two members were as similar as possible in regard to such factors as size and age. The ratio of total loans outstanding to total assets was calculated for each of the banks. For this ratio, the sample mean difference (country x - country y) was 0.0579, and the sample standard deviation of the differences was 0.3086. Test, against a two-sided alternative, the null hypothesis that the two population means are equal. (Assume α = 0.01.) Click the icon to view the critical values of the Student's t distribution. Which of the following correctly states Ho and H₁ ? A. Ho: Mx Hy = 0 H₁: Hx-Hy >0 OC. Ho: Mx Hy ‡0 Hi HxHy=0 - O E. Ho: Mx Hy = 0 H₁: Hx-Hy <0 B. Ho: Mx Hy = 0 H₁: Hx-Hy #0 D. Ho: Hx-Hy = 0 H₁: Hx-Hy 20 OF. Ho: Mx Hy = = 0 H₁: Hx-Hy ≤0
In a study comparing banks in two countries, a sample of 142 matched pairs of banks was formed. Each pair contained one bank from country x and one from country y. The pairings were made in such a way that the two members were as similar as possible in regard to such factors as size and age. The ratio of total loans outstanding to total assets was calculated for each of the banks. For this ratio, the sample mean difference (country x - country y) was 0.0579, and the sample standard deviation of the differences was 0.3086. Test, against a two-sided alternative, the null hypothesis that the two population means are equal. (Assume α = 0.01.) Click the icon to view the critical values of the Student's t distribution. The test statistic is t = 2.236. (Round to three decimal places as needed.) The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.)
Suppose that the blood pressure for a randomly selected patient has an average of 22 and variance of 441. If a sample of 220 patients is selected, then what is P(-1.2 < X< 1.4) ?
Water availability is of prime importance in the life cycle of most reptiles. To determine the rate of evaporative water loss of a certain species of lizard at a particular desert site, 34 such lizards were randomly collected, weighed and placed under the appropriate experimental conditions. After 24 hours, each lizard was removed, weighed, and its total water loss was calculated by subtracting its body weight after treatment from its initial body weight. Previous studies have shown that the relative frequency distribution of water loss for this species of lizard has a mean of 3.1 grams and a s.d. of 0.8 gram b) What is the probability that x is less than 2.7 grams?

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