(Solved): A random variable X has binomial distri- 1. 0 bution with the following properties: I. Var[X]E[X] ...

A random variable $$X$$ has binomial distri- 1. 0 bution with the following properties: I. $$\frac{\mathrm{E}[X]}{\mathrm{Var}[X]}=1.18$$ 2. 1 II. $$\mathrm{Pr}(X=0)=0.444$$ 3. 2 Determine the mode of the random variable 4. The correct answer choice is not given. $$X$$. 5. 3 Emme takes a quiz for her Anthropology 401E course. There are 8 multiple-choice questions on the test with 5 answer choices, only one of which is correct. Emme has not studied for the test, so she just randomly guesses the answers. What is the probability that Emme answers exactly 3 questions correctly? Enter your answer as a decimal with four significant digits.