Problem 1. (12 points) A standard deck of cards has 52 cards, which can be classified as face cards - King, Queen, Jack - and non-face cards. The distribution of face cards and non-face cards is below. Category Face cards Non-face cards Total Frequency 12 40 52 We will perform the experiment of drawing a card with replacement five times. Answer the following questions and show all of your work. (a) (5 points) Let a binomial random variable X = the number of face cards we get from five draws. Study the characteristics regarding this experiment that make X binomially distributed. No credits are given without work. (b) (2 points) Write down the notation of the binomial distribution of X with appropriate parame- ters. (c) (3 points) What is the probability at least three face cards are drawn? Show your work. Answers can be left as fractions. Otherwise, round your final answer to three decimal places. (d) (2 points) What is the number of face cards is expected to be drawn on average, considering all possible five attempts we can make? Show your work. Round your final answer to the next whole number