Consider rolling a die. Determine the mean or expected value of number of spots that would appear.

1. Which value is found at the center of the normal curve? A. mean B. median C. mode D. all of the above 2. What marks the change in the curve's concavity? A. curve B. inflection points C. mean D. standard deviation 3. What is the total area in the distribution under the curve? A. 0 B. 1 C. 2 D.3 4. Which of the following symbols is used to denote the mean? A. o B. H C. a D. . 5. What is another name for normal distribution? A. Gaussian distribution B. Poisson distribution C. Bernoulli's distribution D. Probability distribution 6. Which of the following is a parameter of normal distribution? A. mean B. standard deviation C. mean and standard deviation D. none of the above10 7. What percent of the area under a normal curve is within 2 standard deviations? A. 68.3% B. 95.4% C. 99.7% D. 100% 8. What percent of the area under a normal curve is within 3 standard deviations? A. 68.3% B. 95.4% C. 99.7% D. 100% 9. Which of the following does not describe a normal curve? A. asymptotic B. bell-shaped C. discrete D. symmetrical about the mean 10. What percent of the area under a normal curve is within 1 standard deviation? A. 68.3% B. 95.4% C. 99.7% D. 100%\fSteps Solution 1 Construct the probability distribution Number of Spots X for the random variable X representing Probability P(X) the number of spots that would appear. 2. Multiply the value of the random variable X by the corresponding probability. Number of Spots X Probability P(X) X.P(X) 3. Add the results obtained in Step 2. Number of Spots X Probability P(X) X.P(X) H=[ XP(X) = Interpret the result: 0.75. 0.17. 0.04, 0.02