(Solved): Part I. Multiple-choice questions (45 Points, 3 each with no partial credits) 1. A sample space con ...

Part I. Multiple-choice questions (45 Points, 3 each with no partial credits) 1. A sample space contains only five values: \( x=0,1,2,3,4 \). Which of the following could be its probability distribution, Assume that the sets of the probabilities corresponds to the \( x \)-values. \( \begin{array}{ll}\text { I. }\{0.3 ; 0 ; 0.3 ; 0 ; 0.4\} & \text { II. }\{0 ; 0 ; 0 ; 0 ; 1\}\end{array} \) III. \( \{0.1 ; 0.2 ; 0.3 ; 0.4 ; 0.1\} \) (A) I only (B) I and II (C) I and III (D) I, II, and III Question \#2-4 are based on the following information: A continuous random variable \( x \) has a normal distribution with the mean of 80 and standard deviation of 10 . 2. The probability of \( x=80 \) is: (A) 0 (B) \( 0.5 \) (C) 1 (D) \( { }^{10} / 80=0.125 \) 3. If the \( z \) score for \( x \) is negative, then which of the following is not true? (A) \( x \) is less than 80 . (B) \( x \) cannot be greater than or equal to the mean. (C) \( x \) may be below 42 . (D) \( x \) is less than or equal to 80 4. To find the probability that the \( x \)-value is greater than 90 , you shade the region under the bellcurve, with \( \mu=80 \) in the middle, from \( x=90 \) (A) to the left (B) to the right (C) to 0 (D) to 80 5. Which of the following statement is true to determine whether Events \( \mathrm{A} \) and \( \mathrm{B} \) are independent? (A) Independent, because \( P(A \cap B)-P(A) \times P(B)=0.07-0.23 \times 0.26=0.0102<5 \% \). (B) Independent, because 7 subjects under 20 in favor of Baseball. (C) Independent, because they are different categories. (D) Dependent, because there are 7 subject in common.