-) Mrs. G is very good at Sudoku puzzles. 75% ofin( @time, she can complete a puzzle in under 10 minutes, Her class challenges her to test this seems's success rate by completing 10 puzzles. a) Define a random variable X and show that it follows b) Complete the probability distribution below. a binomial distribution. X P(X) P = 75% /0.75 0 9. 53 x 10-7 n = 10 1 2. 86 x 10 5 x = 0-10 2 3. 86 x 10-4 3 0.003 X 10 4 10. 01 x 10 5 0105 X 10 6 0 . 14 x 10 7 0. 25 x 10 8 0. 28 X 10 19 0. 18 x 10 10 10.056X 10 c) Find and interpret the expected value. d) Find and interpret the standard deviation. e) If.Mrs. G completes all 10 puzzles in under 10 minutes each, would you be suspicious of her cheating? explain why or why not using probability