a) Let P(A|B) : 0.2. What event has probability 0.8? A) P(A) 13) HE C) P(ACIB) D) P(AIBC) E) P(ACIBC) b) Given events A and B are independent with P(A) : 1/3 and P(B) : 1/2, which of the following conditions could exist? A) P(A and B) = 1/12 B) P(BEA) = 1/3 C) P(A|BC) = 2/3 D) P(AC|B) = 2/3 c) Which of the following is true about any discrete random X '? A) The expected value (also called the mean) of X is np. B) The sum of all possible values of X is equal to one. C) The probabilities associated with all the possible values of X sums to one. D) The probability distribution of X is bell-shaped and symmetric. E) Approximately 95% of the values of X fall within two standard deviations of the mean. (1) Which of the following can be expected to be Binomially distributed? A) The number of phone calls a customer service rep can answer in an hour. B The number of employees at a start-up that call in sick tomorrow (it is known to have 30 employees). The amount of money a customer spend at Amazon.com. ) C) D) The average length of time a sample of 30 customers take to checkout at a website. E) The number of iPhones that fail in the rst year in a random sample of 50 iPhone Xs. e) Why is the central limit theorem important in statistics? A) Because for a large sample size n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. B) Because for a large sample size n, it says the population is approximately normal. C) Because for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. D) Because for any sample size n, it says the sampling distribution of the sample mean is approximately normal. f) Let X be normally distributed with mean 20 and standard deviation 5. Determine: i) P(X