The table shows projections for the Year 2015 2040 2055
female population of a country (in Female Population
180
231 258
millions).
(a) Find a quadratic function f(x) = ax2 + bx + c that gives the female population in
millions) in year x, where x = 0 corresponds to the year 2000.
(b) Estimate the female population in the year 2050.
(a) The coefficient of x? in the equation is a =
(Do not round until the final answer. Then round to three decimal places as needed.)
The coefficient of x in the equation is b=
(Do not round until the final answer. Then round to one decimal place as needed.)
The constant in the equation is c= | 0
(Do not round until the final answer. Then round to one decimal place as needed.)
(b) The estimate for the female population in the year 2050 is million.
(Use the answer from part (a) to find this answer. Round to the nearest integer as
needed.)

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?