8. The proportion of impurities per batch in a chemical product is a random variable that is well modeled by a Beta distribution with a-3 and -2. A batch with more than 40% impurities cannot be sold. a. Find the probability that a randomly selected batch cannot be sold because of excessive impurities b. What is the mean proportion of impurities? the variance? (Hint: use an appropriate method) 9. Suppose Y the amount spent on electricity (in dollars) per month for residents has a mean of $83 and a standard deviation of S11. A random sample of 20 resident's electricity bills is found. Approximate the probability the sample mean electricity bill is less than $80