There are 6 areas of land for sale. Land 1 has 306 acres and Land 2 has 123 acres. Cattle used to stay on Land 3 and pigs on Land 4. A rancher is looking to buy some land for his horses and cattle. Land 3 has 451 acres and is right next to Land 1. Land 1 and 4 are worth $1,000 an acre. Land 3 and 6 are $1,250 an acre. Taxes are already included in the price per acre. The rancher owns 11 horses and 28 cattle and wants at least 500 acres. If the rancher buys Land 1 and 3, how much does he need to pay? Do not include $ in your answer. For example, if your answer is $19, enter 19.

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?