--%>
Assignment Help - homework help

Probability Distributions and Data Modeling

1. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approximation to the binomial and compare your answers.

2. The number and frequency of Atlantic hurricanes annually from 1940 through 2007 is shown here.

NUMBER    0 1 2 3 4 5 6 7 8

Frequency 5 16 19 13 3 5 4 2 1

a) Find the probabilities of 0-8 hurricanes each season using data.

b) Assuming a Poisson distribution and using the mean number of hurricanes per season from the empirical data, compute the probabilities of experiencing 0-8 hurricanes in a season.

Compare these to your answer to part (a). How good does a Poisson distribution model this phenomenon?

3. The distribution of SAT scores in math for an incoming class of business students has a mean of 580 and standard deviation of 25. Assume that the scores are normally distributed.

  1. Find the probability that an individual's score is less than 550.
  2. Find the probability that an individual's score is between 560 and 600.
  3. Find the probability that an individual's score is greater than 620.
  4. What % of students will have scored better than 700?
  5. Find the standardized values for students scoring 500, 600, and 700 on the test.

4. Historical data show that customers who download music from a popular web service spend approximately $20 per month, with a standard deviation of $4. Find the probability that a customer will spend at least $15 per month. If the company samples 100 customers, find the mean and standard deviation of the number who spend at least $15 per month. What is the probability that at least 40% of them will spend a t least $15 per month?

 

   Related Questions in Advanced Statistics

  • Q : Describe what happens to the confidence

     A nurse practitioner working in a dermatology clinic is studying the efficacy of tretinoin in treating women's post partum abdominal stretch marks.  From a sample of 15 women, the mean reduction of stretch mark score is -0.33 with a sample standard deviation of 2.46.  Describe wha

    		•
  • Q : Conclusion using p-value and critical

    A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evid

    		•
  • Q : How you would use randomization in

    The design of instrument controls affects how easily people can use them. An investigator used 25 students who were right-handed to determine whether right-handed subjects preferred right-handed threaded knobs. He had two machines that differed only in that one had a

    		•
  • Q : Probability and Statistics

    Instructions: Do your work on this question and answer sheet. Please print or write legibly, and, as always, be complete but succinct. Record your answer and your supporting work in the designated space. Explain your method of solution and be sure to label clearly any

    		•
  • Q : Problem on layout A manufacturing

    A manufacturing facility consists of five departments, 1, 2, 3, 4, and 5. It produces four components having manufacturing product routings and production volumes indicated below.   1. Generate the from-to matrix and the interaction matrix. Use a

    		•
  • Q : Analytical Report Hi I WOULD LIKE TO

    Hi I WOULD LIKE TO KNOW IF YOU CAN HELP ME TO DO THE ASSIGNMENT IN HEALTH STATISTICS THANKS

    		•
  • Q : Random variables Random variables with

    Random variables with zero correlation are not necessarily independent. Give a simple example.    

    		•
  • Q : Components of time series Name and

    Name and elaborate the four components of time series in brief.

    		•
  • Q : Describe how random sampling serves

    Explain sampling bias and describe how random sampling serves to avoid bias in the process of data collection.    

    		•
  • Q : Grouped Frequency Distributions Grouped

    Grouped Frequency Distributions: Guidelines for classes: A) There must be between 5 to 20 classes. B) The class width must be an odd number. This will assure that the class mid-points are integers rather than decimals. C) The classes should be mutually exclusive. This signifies that no data valu

    		•