Which of the following is correct about a probability distribution? Sum of all p

Question

Which of the following is correct about a probability distribution? Sum of all possible outcomes must equal 1 Outcomes must be mutually exclusive and collectively exhaustive Probability of each outcome must be between 0 and l inclusive All of the above A market research team compiled the following probability distribution, where x represents the number of times per week students eat at the CSUSB Commons cafeteria. The mean (expected value) of x is _____. 1.0 1.5 2.0 2.5 Consider once again the data from question #13 above. What is the standard deviation of the number of times per week students eat at the cafeteria? 0.80 0.89 1.00 2.00 It's question #13 again. What proportion of students eat at the cafeteria at least twice a week? 0.50 0.70 0.30 0.80 One last time...consider the data from question #13. Which of the following is true? This distribution is skewed to the right. This is a binomial distribution. This is a normal (bell shaped) distribution. This distribution is skewed to the left. If x is a binomial random variable with 8 trials and a 60% chance of success, what is the standard deviation? 4.8 3.2 1.92 1.39

Explanation / Answer

12) Option-D)

13) Mean = E(X) = 0 * 0.1 + 1 * 0.1 + 2 * 0.5 + 3 * 0.3 = 2

Option-C)

14) E(X2) = 02 * 0.1 + 12 * 0.1 + 22 * 0.5 + 32 * 0.3 = 4.8

Var(X) = E(X2) - (E(X))2

           = 4.8 - 22

           = 0.8

Standard deviation = sqrt(0.8) = 0.89

Option-B)0.89

15) P(X > 2) = P(X = 2) + P(X = 3)

                     = 0.5 + 0.3

                     = 0.8

Option-D)0.8

16) Option-D)

17) n = 8

p = 0.6

Standard deviation = sqrt(n * p * (1 - p)) = sqrt(8 * 0.6 * 0.4) = 1.39

Option-D

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