Question 1 Assume that the expectation of the binomial random variable X is 16 and that the standard deviation is 4. Find: P{X>14}-Question 7 15 points Save An An unexperienced technician has mixed 6 rechargeable AAA batteries with 30 regular AAA batteries. After this accident, the technician has to find all of the rechargeable batteries by using a special battery tester, which can accommodate 4 batteries at once. Assume that the number of the rechargeable batteries found in each test is a random variable X. Find the variance of X.Question 4 X1, X2, ..., Xn are Gamma distributed random variables, where a=4 and A=0.4. Find P(X24).Question 5 X~Xn"are Chi-Square distributed random variables, where n=8. Find P{X24).Question 2 10 points Save Answer The number of years a radio functions is exponentially distributed with the parameter A = 1/14. If Jones buys a 3-year-old used radio, what is the probability that it will be working when this radio will be 8 years old?Question 3 15 points Save Answer Let's assume that the lifetimes of current brand AAA batteries are normally distributed, where mean is 60 hours and variance is 16. Find the probability that the lifetime of one randomly chosen battery of that brand would be outside of the interval 58 - 62 hours