Homework #8 Probability Distribution 1. Determine if the following are probability distributions (if no, state why). a. X 3 6 9 12 15 P(X) 1/\"? 2/7 If? U7 U7 b.X 1 2 3 4 5 P(X) 3a; US 1/8 U8 1/4 2. Construct a probability distribution for the data: ([Tse two decimal places) a. A die is loaded in such a way that the probabilities of getting l._ 2, 3. 4. 5, and 6 are 2;\"25. 2f25. 3:10. 1:10. 3:10. and 325 respectively. x P(X) 0.08 0.08 0.3 0.1 0.3 0.12 UI-IEWNrI a 3. Below is a probability distribution for the number of math failures of BC students. Complete the blank considering you have a probability distribution. X 0 1 2 3 4 P(X) 0.21 0.24 0.07 0.08 a. P(X=2)= b. What is the probability to have at least two math failures? c. What is the probability to have at most one math failures? (:1. What is the probability to have no more than two math failures? e. What is the probability to have one or two math failures? Mean, Variance, and Standard Deviation 4. From past experience, a company has found that in carton of transistors, 86% contain no defective transistors, 7% contain one defective transistor, 4% contain two defective transistors, and 3% contain three defective transistors. (Express your final answers using two decimal places) a. Construct a probability distribution below. X P(X Mean= Variance= St. Dev. = b. Find the mean, variance, and standard deviation for the defective transistors. 5. The number of suits sold per day at Suit World is shown in the probability distribution below. (Express your final answers using two decimal places) X 23 26 19 15 21 P(X) 0.2 0.2 0.3 0.2 0.1 X P(X) Mean= Variance= St. Dev.= a. Find the mean, variance, and standard deviation of the distribution