Math

StatisticsQ&A LibraryHurricanes. In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 6.1 per year, as in Example 1; and proceed to find the indicated probability.Hurricanesa. Find the probability that in a year, there will be 5 hurricanes.b. In a 55-year period, how many years are expected to have 5 hurricanes?c. How does the result from part (b) compare to the recent period of 55 years in which 8 years had 5 hurricanes? Does the Poisson distribution work well here?Question

Asked Jan 12, 2020

1 views

Hurricanes. In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 6.1 per year, as in Example 1; and proceed to find the indicated probability.

Hurricanes

a. Find the probability that in a year, there will be 5 hurricanes.

b. In a 55-year period, how many years are expected to have 5 hurricanes?

c. How does the result from part (b) compare to the recent period of 55 years in which 8 years had 5 hurricanes? Does the Poisson distribution work well here?

Step 1

Define the random variable *x* as the number of hurricanes in a year. Here, the occurrence of hurricanes is random and each hurricane is independent of the other. Also, the occurrences (hurricanes) are uniformly distributed for every year. Then, *x* follows Poisson distribution.

The Poisson distribution formula is,

Step 2

Step 3

**b.**

From part (a), the probability to have 5 hurricanes in a year is 0.158.

For a 55-year ...

Tagged in

Find answers to questions asked by student like you

Q: Sleep Notation Consider a sample of sleep times taken from the population of all adults living in Al...

A: The symbols used for the sample mean, population mean, sample standard deviation, population standar...

Q: How would I solve this problem?

A: (a)The level of significance 1% since α is given as 0.01.The null and the alternative hypotheses are...

Q: In each of Exercises, decide whether or not the two events in question are independent or whether it...

A: If two events A and B are independent then,

Q: In each of Exercises the events A1, A2, . . . are mutually exclusive and exhaustive. We have provide...

A: From the Bayes’ theorem, the conditional probability is given as follows.

Q: Car Fatalities The recent rate of car fatalities was 33,561 fatalities for 2969 billion miles travel...

A: Mean of Poisson distribution:The formula is given by,

Q: In each of Exercises, decide whether or not the two events in question are independent or whether it...

A: Independent event

Q: True–False Tests. A student takes a true–false test consisting of 15 questions. Assume that the stud...

A: Introduction to binomial distribution:Consider a random experiment involving n independent trials, s...

Q: Change for a Quarter How many different ways can you make change for a quarter? (Different arrangeme...

A: Formulas related to unit conversion:

Q: Nuts and Bolts. A hardware manufacturer produces nuts and bolts. Each bolt produced is attached to a...

A: a)

Q: In each of Exercises, decide whether or not the two events in question are independent or whether it...

A: Independent event

Q: Determine the value of each quantity. a.7C3b.5C2c.8C4d.6C0e.9C9

A: Combination Rule:There are n different items and r number of selections and the selections are made ...

Q: Birth Weights Based on Data Set 4 “Births” in Appendix B, newborn males have weights with a mean of ...

A: z score for the male:Let X be the weight for newborn males.The formula for the z score is,

Q: In Exercises, we have provided simple data sets for you to practice the basics of finding measures o...

A: a.Computation of mean:The value of mean is obtained as 5, from the calculations given below:

Q: ESP Experiment. A person has agreed to participate in an extrasensory perception (ESP) experiment. H...

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for y...

Q: The mean height of women in a country (ages 20 - 29) is 63.5 inches. A random sample of 60 women in ...

A: It is given that the mean is 63.5 and the standard deviation is 2.75.

Q: Suppose that A and B are events such that P(A) = 2/7 and P(A&B) = 3/25. Determine P(B| A)

A: The formula for conditional probability is,

Q: The probability is 0.314that the gestation period of a woman will exceed 9 months. In 4000 human ges...

A: The number of gestation period will exceed 9 months can be obtained as follows:Event E denotes that ...

Q: Identifying Probability Distributions. In Exercises 7–14, determine whether a probability distributi...

A: Requirements:The following requirements should be satisfied for the distribution to follow probabili...

Q: Online Medical Info USA Today posted this question on its website: “How often do you seek medical in...

A: Voluntary response sample:If the sample made up of volunteers or self-selected participants, then th...

Q: Suppose x has a distribution with a mean of 70 and a standard deviation of 15. Random samples of siz...

A: Click to see the answer

Q: Net Worth. The Board of Governors of the Federal Reserve System publishes information on family net ...

A: Here, there is possible for the mean net worth of family to be higher. Because there is presence of ...

Q: Suppose that C and D are events such that P(C) = 4/5 and P(C&D) = 3/10. Find P(D| C).

A: The formula for conditional probability is,

Q: Suppose that C and D are independent events such that P(C) = 0.7 and P(D) = 0.6. Find P(C&D).

A: The Special Multiplication Rule (for two independent event)

Q: Distribution of Wealth In recent years, there has been much discussion about the distribution of wea...

A: To check the distribution of amount of wealth of 3000 randomly selected adults, Histogram will be pl...

Q: Scatterplot What is a scatterplot and how does it help us?

A: Scatterplot is a graph which shows the relationship between two quantitative variables. It is graph ...

Q: Drawing Cards. Two cards are drawn at random from an ordinary deck of 52 cards. Determine the probab...

A: a)The General Multiplication Rule:

Q: Avogadro Constant If you are asked on a quiz to give the first (leftmost) nonzero digit of the Avoga...

A: Given info:Guessing the first nonzero digit of the Avogadro constant.

Q: Playing Golf. From the National Golf Foundation and the U.S. Census Bureau, we obtained the followin...

A: a)Rule of Total Probability

Q: Composite Water Samples The Fairfield County Department of Public Health tests water for contaminati...

A: The probability of a randomly selected public swimming area contains bacteria is 0.005. The probabil...

Q: SAT Test.In Exercises 15–20, assume that random guesses are made for eight multiple choice questions...

A: From the given information, the value of n is 8 and the probability of correct answer is 0.20.The ra...

Q: Random Digits Computers are commonly used to randomly generate digits of telephone numbers to be cal...

A: A nonstandard normal distribution cannot be used because the randomly generated digits themselves do...

Q: Health Test In an investigation of a relationship between systolic blood pressure and diastolic bloo...

A: Scatter plot shows the relationship between the two quantitative variables. It shows whether relatio...

Q: Identify the notation used for each of the following concepts. a.k factorialb. The number of possibl...

A: a.Factorial Rule:The total number of ways k different objects can be arranged where order of the obj...

Q: Geometric Distribution If a procedure meets all the conditions of a binomial distribution except tha...

A: In the National Health and Nutrition Examination Survey conducted by the National Center for Health ...

Q: How would I solve for (b), Z value, and p-value?

A: (b) Sampling distribution:Here, it is assumed that x has a normal distribution and σ=0.64. That is, ...

Q: At Least One Correct Answer If you make random guesses for 10 multiple choice SAT test questions (ea...

A: It is given that there are 10 multiple choice questions, a student makes a random guess among the fi...

Q: Social Networking In a Pew Research Center survey of Internet users, 3732 respondents say that they ...

A: Solution: We are given that:3732 respondents say that they use social networking sites and 1380 resp...

Q: Voluntary Response Data If we have a large voluntary response sample consisting of weights of subjec...

A: A voluntary response sample can be defined as the sample which is made up of people who are particip...

Q: Insomnia Treatment A clinical trial was conducted to test the effectiveness ofthe drug zopiclone for...

A: Click to see the answer

Q: Calculus Pretest. Students are given three chances to pass a basic skills exam for permission to enr...

A: Given that,Sixty percent of the students pass on the first try; of those that fail on the first try,...

Q: There are 80 questions from an SAT test, and they are all multiple choice with possible answers of a...

A: The total number of question = n = 80probability of correct answer = 1/5 = 0.2The mean is calculated...

Q: A study is conducted to determine whether people learn better with spaced or massed practice. Subjec...

A: 1)When the subjects are not randomly sampled from the specified population, there will be will be a ...

Q: Give an example of the conditional probability of an event being the same as the unconditional proba...

A: Independent eventIf two events A and B are independent then the conditional probability of an event ...

Q: Computers As a quality control manager at Texas Instruments, you find that defective calculators hav...

A: Histogram:The histogram is a univariate graphical representation where a numerical variable is graph...

Q: Measures of Center In what sense are the mean, median, mode, and midrange measures of “center”?

A: Measure of central tendency is a single value which attempts to describe a dataset by locating a cen...

Q: 13. Favorite Coffee Flavor A survey was taken asking the favorite flavor of a coffee drink a person ...

A: There are 50 persons participated in the given survey.

Q: Housing Units. The U.S. Census Bureau publishes data on housing units in American Housing Survey for...

A: Note:Hey there! Thank you for the question. As you have posted a question with more than 3 parts, ac...

Q: Social Networking Based on data from the Pew Internet Project, 74% of adult Internet users use socia...

A: The probability of getting an adult Internet user who uses the social networking sites is 74%.

Q: iOS Marketshare You plan to develop a new iOS social gaming app that you believe will surpass the su...

A: (a)Step-by-step procedure to obtain the value of z using MINITAB:Choose Graph > Probability Distr...

Q: Telephone Numbers. In the United States, telephone numbers consist of a three-digit area code follow...

A: a. Computation of number of possible different area codes:The number of possible different area code...