Please help with test prep.Show work to explain.

1.The mean lifetime for a car battery is 180 weeks, with a standard deviation of 15 weeks. Assuming a normal distribution, what is the probability that the measured lifetime of a randomly chosen car battery is greater than 210 weeks ?

2.Two balls are drawn in succession, without replacement, out of a box containing 5 red and 3 white balls.What is the probability that the first ball drawn is white and the second ball drawn is red?

3.A bakery is contracted to bake cakes for grocery stores to sell. The bakery's daily production costs are $1.40 per cake baked plus a fixed cost of $527. The cakes are sold by the grocery stores for $7.60 each. How many total cakes must be sold daily for the bakery to break even?

4.Use the following information to answer parts a-c.

U = {a, b, c, d, e, f, g, h, i, j,}; A = {a, c, e, g, i}; B = {b, d, f, h, j}; C = {a, b, d}

a. Determine ???????? : ___________________________________

b. Determine (????????)(????????) : ___________________________________

c. Determine ???????? : ___________________________________

5.Fifteen people work in an office. 8 are women and 7 are men. The flu virus is coming.

(a) In how many ways can the flu virus randomly select 7 workers out of the 15 to get sick? Show work.

(b) In how many ways can the flu choose 7 workers, if 3 must be women and 4 must be men? Show work.

(c) If the flu virus randomly selects 7 workers from the 15 in the office, what is the probability that 4 are men and 3 are women? Round answer to nearest ten-thousandth (4 places after decimal). Show work.

6.Solve the system of equations using substitution, elimination by addition, or augmented matrix methods (your choice). Show work.

9????8????= 93

4????+5????= 10

7.A freight-hauling firm estimates that it will need a new forklift in six years. The estimated cost of the vehicle is $40,000. The company sets up a sinking fund that pays 8% compounded semiannually, into which it will make semiannual payments to achieve the goal. Calculate the size of the payments.

8.A recent poll of voters showed that 50% of them support the mayor. What is the probability that in a random sample of 16 voters, exactly 8 of them support the mayor ? Show Work

9.A marketing survey of 2000 randomly-selected convenience store customers found that 1415 of them bought a glazed donut yesterday. 1605 said they bought a frosted crme-filled donut yesterday. 180 customers said they bought neither yesterday.

(a) What is the probability that a single randomly-selected customer bought only a frosted crme-filled donut yesterday? Round answer to nearest hundredth. Show work