2. The incomplete probability distribution table at the right is of the discrete

Question

2. The incomplete probability distribution table at the right is of the discrete random variable x representing the number of times people donate blood in 1 year. Answer the following: x P(X=x) (a) Determine the value that is missing in the table. (Hint: what are the requirments for a probability distribution?) 0 0.632 0.064 1 0.084 2 0.013 (b) Find the probability that x is at least 2 , that is find P(x 2). 3 0.025 4 0.059 5 (c) Find P(x 1). Describe what the resulting value represents within the given context. 6 0.123 0.936 0.936-1=0.064 (d) Find the mean (expected value) and standard deviation of this probability distribution. (e) Explain what a “sampling distribution of sample means” is. Be specific!

Explanation / Answer

b) P(X > 2) = 1 - [P(X = 0) + P(X = 1)] = 1 - [0.632 + 0.084] = 0.284

c) P(X < 1) = [P(X = 0) + P(X = 1)] = [0.632 + 0.084] = 0.716

d) E(X) = 0 * 0.632 + 1 * 0.084 + 2 * 0.013 + 3 * 0.025 + 4 * 0.059 + 5 * 0.064 + 6 * 0.123 = 1.479

E(X2) = 02 * 0.632 + 12 * 0.084 + 22 * 0.013 + 32 * 0.025 + 42 * 0.059 + 52 * 0.064 + 62 * 0.123 = 7.333

Var(X) = E(X2) - (E(X))2 = 7.333 - 1.4792 = 5.1456

Standard deviation = sqrt(5.1456) = 2.268

e)If we draw all possible samples of size n from a given population, this statistic is called a sampling distribution.

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