--%>
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 : 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 : Problem on consumers marginal utility

    Consider a consumer with probability p of becoming sick.  Let Is be the consumer’s income if he becomes sick, and let Ins be his income if he does not become sick, with Is < Ins. Suppo

    		•
  • Q : What is your statistical decision

    Question 1 Do parents with more children travel more than parents of small families? To find out, a survey was done of a large number of adults. Respondents were asked how many children they had and how many times

    		•
  • Q : Frequency Distributions Define the term

    Define the term Frequency Distributions?

    		•
  • Q : Find the cumulative distribution

    You must use the pre-formatted cover sheet when you hand in the assignment. Out full detailed solutions. Sloppy work will naturally receive a lower score. 1. Suppose at each step, a particle moving on sites labelled by integer has three choices: move one site to the right with pro

    		•
  • Q : Problem on Chebyshevs theorem 1. Prove

    1. Prove that the law of iterated expectations for continuous random variables.2. Prove that the bounds in Chebyshev's theorem cannot be improved upon. I.e., provide a distribution which satisfies the bounds exactly for k ≥1, show that it satisfies the

    		•
  • Q : Probability problem A) What is the

    A) What is the probability of getting the following sequence with a fair die (as in dice):B) What is the probability of getting the same sequence with a die that is biased in the following way: p(1)=p(2)=p(3)=p(4)=15%;

    		•
  • 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 signaling Quality

    Quality control: when the output of a production process is stable at an acceptable standard, it is said to be "in control?. Suppose that a production process has been in control for some time and that the proportion of defectives has been 0.5. as a means of monitorin

    		•
  • 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

    		•