In a large Insurance Company in U. S., people over age thirty five have an annual income that follows a normal distribution with mean 70,000 and standard deviation 9,000. The incomes of those under age thirty five are also approximately normal, but with mean 45,000 and standard deviation 8,000. With the above information simulate 10000 employees over 35 and 10000 employees under 35 and answer the questions.
1) What is the approximate probability that a randomly picked, employee over 35 will have an income lower than or equal to 60,000? Pick the closest answer.

a) About 15%
b) About 25%
c) About 35%
d) About 55%

2) What would be a range [A to B] for the income, which would contain 95% of the employee under 35? Pick the closest answer.

a) Between 35,000 and 65,000
b) Between 29,000 and 61,000
c) Between 52,000 and 88,000
d) Between 35,000 and 60,000

If you shift the linear parent function, f(x)=x, up 13 units, what is the equation of the new function?

Percent increase and decrease. original number: 45 new number: 18

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.