--%>
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 : 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 : Discrete and continuous data

    Distinguish between discrete and continuous data in brief.

    		•
  • Q : Non-parametric test what is the

    what is the appropriate non-parametric counterpart for the independent sample t test?

    		•
  • Q : Calculate corresponding t value or s

    1)    Construct a 99% confidence interval for the population mean µ.   2)    At what significance level do the data provide good evidence that the average body temperature is

    		•
  • Q : MANOVA and Reflection Activity 10:

    Activity 10: MANOVA and Reflection 4Comparison of Multiple Outcome Variables This activity introduces you to a very common technique - MANOVA. MANOVA is simply an extension of an ANOVA and allows for the comparison of multiple outcome variables (again, a very common situation in research a

    		•
  • Q : Statistics A nurse practitioner working

    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 what happens to the c

    		•
  • 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 : Problem on income probability Kramer

    Kramer spends all of his income  $270  on two products, soup (S) and on golf balls (G). He always bought 2 golf balls for every 1 cup of soup he consumes. He acquires no additional utility from the other cup of soup unless he as well gets 2 more golf balls a

    		•
  • 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

    		•