Please see below picture. Questions a, b, c, d: all part of main question 5.

5. Information: Even though it has been over 40 years since Elvis Presley died, 10% of the letters that come through the post office near Graceland are addressed to Elvis. Suppose that a random sample of n=30 letters arriving at the post office is selected. Let the random variable X denote the number of letters in the sample that are addressed to Elvis. a) What kind of a distribution does X have? (Select one): A. Bernoulli Distribution B. Exponential Distribution C. Discrete Uniform Distribution D. Binomial Distribution E. Normal Distribution b) In a random sample of thirty letters, what is the expected number of letters addressed to Elvis? (Round the value to one decimal place). c) What is the variance of the distribution of X? Round the value to one decimal place. d) In a random sample of thirty letters, what is the probability that at least one letter is addressed to Elvis? Calculate the probability using the exact distribution. (Round the probability value to four decimal places)