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Statistics Assignment

  1. Construct a set of four numbers that have mean 12, mode 10, and median 11. Explain.
  2. Suppose we have a data of size two, say x1 and x2 whose mean is 6. If x1=3, compute the value of x2.
  3. Assume that we have a data of size 3 with mean 6 and mode 3. Compute the standard deviation.
  4. A data set is formed by recording the sums in 400 rolls of a pair of a dice. A second data set is formed by recording the results of 600 draws of a ball from a box containing 11 balls numbered 2 through 12. Which of the data sets would you expect to have a smaller standard deviation? Explain.
  5. A given binomial distribution has 100 trials and probability of success p=1/5. Compute the standard deviation and explain your solution.
  6. Let z=a be a positive z-score in a standard normal distribution such that the area between z=-a and z=a is 0.25. What is the area for z<-a? Explain.
  7. Find the area under the standard normal curve between z=-1 and z=2. Explain your solution.
  8. A given binomial experiment has n=100 trials and p=1/4. Is it more likely to get x=15 successes or x=40 successes. Why?
  9. Determine if checking 500 applicants to see if they were admitted to Park University is a binomial experiment or not. Explain.
  10. Two fair dice are rolled at once. Find the conditional probability that the sum is 6, given that the sum is an even number.
  11. Consider a box with 5 red and 3 blue balls. Two balls are drawn at random. If it is known that the first one is red, then what is the probability that the second one is red?
  12. Consider a box with 6 red and 5 blue balls. If three balls are drawn at random, what is the probability that at least one of them is blue?
  13. Suppose we have an urn that contains 5 white and 11 red balls. Two balls are drawn in succession without replacement. If the second ball is white, what is the probability that the rst ball was white?
  14. Approximately 1% of women aged 40-50 have breast cancer. A woman with breast cancer has a 80% chance of a positive test from a mammogram, while a woman without has a 20% chance of a false positive result. What is the probability a woman has breast cancer given that she just had a positive test?
  15. Suppose that an event A has a probability 0.4. Suppose moreover that P(B|A) = 0.3 and P(B|A’) = 0.6. Find P(A’ U B).
  16. A box with 21 flashbulbs contains 5 defective ones. A random sample of two is selected and tested. Let X be the random variable associated with the number of defective bulbs. Find the probability distribution and the expected value of X.
  17. A random variable has range x1, x2, and x3 all with equal probabilities. What is E(X)?
  18. Let S be a given sample space and let E and F be two events that have no common outcome and their union is S. If P(E)=0.3, then find P(F).
  19. Given the following data: 2, 2, 4, 5, 8, 8, 8. What is the mode, median, and the mean? Explain.
  20. Explain why the variance is never negative.
Suzie Mercy

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Suzie Mercy
6 years ago

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