Please answer 11-16

11. (6 points) The average height of women is 64 inches. The standard deviation is 2 inches. The heights have a normal distribution. Find the probability that a randomly selected woman is between 58 and 70 inches tall. 12. (6 points) Consider the probability distribution below. Find mean, variance, and standard deviation. k Pr( X=k) -30 12 0 10 30 13. (6 points) A fair coin is tossed 150 times. Find the probability of observing less than 70 heads. 14. (6 points) Barbara knows that she will need to buy a new car in 4 years. The car will cost $20,000 by then. How much should she invest now at 7% compounded monthly, so that she will have enough to buy a new car? 15. (6 points) Calculate the rent of a decreasing annuity at 6% compounded monthly if payments are made every month for 15 years and the present value is $300,000. Round to the nearest cent. 16. (6 points) You buy a car with a down payment of $3000 and payments of $400 per month for 3 years. If the interest rate is 4% compounded monthly, what is the total cost of the car