--%>
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 : 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 : Variation what are the advantages and

    what are the advantages and disadvantages of seasonal variation

    		•
  • Q : Correlation Define the term Correlation

    Define the term Correlation and describe Correlation formula in brief.

    		•
  • Q : Components of time series Name and

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

    		•
  • Q : Problem on Poisson distribution The

    The number of trucks coming to a certain warehouse each day follows the Poisson distribution with λ= 8. The warehouse can handle a maximum of 12 trucks a day. What is the probability that on a given day one or more trucks have to be sent away? Round the answer

    		•
  • 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 : Probability of winning game Monte Carlo

    Monte Carlo Simulation for Determining Probabilities 1. Determining the probability of winning at the game of craps is difficult to solve analytically. We will assume you are playing the `Pass Line.'  So here is how the game is played: The shooter rolls a pair of

    		•
  • Q : Bayesian Point Estimation What are the

    What are the Bayesian Point of estimation and what are the process of inference in Bayesian statistics?

    		•
  • Q : Analyse the statistics of the data

    Assigment Question Select any two manufacturing companies and formulate the cost and revenue functions of the companies. analyse the statistics of the data and then sketch the functions and determine their breakeven points. (Note: You are required to interview the production and sales manag

    		•
  • Q : Problem on utility funtion probability

    Suppose that your utility, U, is a function only of wealth, Y, and that U(Y) is as drawn below. In this graph, note that U(Y) increases linearly between points a and b.  Suppose further that you do not know whether or not you

    		•