Statistics Assignment
- Construct a set of four numbers that have mean 12, mode 10, and median 11. Explain.
- Suppose we have a data of size two, say x1 and x2 whose mean is 6. If x1=3, compute the value of x2.
- Assume that we have a data of size 3 with mean 6 and mode 3. Compute the standard deviation.
- 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.
- A given binomial distribution has 100 trials and probability of success p=1/5. Compute the standard deviation and explain your solution.
- 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.
- Find the area under the standard normal curve between z=-1 and z=2. Explain your solution.
- 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?
- Determine if checking 500 applicants to see if they were admitted to Park University is a binomial experiment or not. Explain.
- Two fair dice are rolled at once. Find the conditional probability that the sum is 6, given that the sum is an even number.
- 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?
- 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?
- 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?
- 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?
- 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).
- 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.
- A random variable has range x1, x2, and x3 all with equal probabilities. What is E(X)?
- 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).
- Given the following data: 2, 2, 4, 5, 8, 8, 8. What is the mode, median, and the mean? Explain.
- Explain why the variance is never negative.
