Given that z is a standard normal random variable, compute the following probabilities. Please draw the
standard normal PDF and shade the area that you are
computing in each case.
A) i) P(Z < -1) ii) P(-3 SZso)
B) Suppose x comes from a normal distribution with mean
20 and variance 144; show that P(x250) is the same as
P(X<-10). What does this prove?

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.

Kumar consulting operates several stock investment portfolios that are used by firms for investment of pension plan assets. last year, one portfolio had a realized return of 12.6 percent and a beta coefficient of 1.15. the average t-bond rate was 7 percent and the realized rate of return on the s& p 500 was 12 percent. what was the portfolio's alpha?

Bayside coatings company purchased waterproofing equipment on january 2, 20y4, for $190,000. the equipment was expected to have a useful life of four years and a residual value of $9,000. instructions: determine the amount of depreciation expense for the years ended december 31, 20y4, 20y5, 20y6, and 20y7, by (a) the straight-line method and (b) the double-declining-balance method. also determine the total depreciation expense for the four years by each method. depreciation expense year straight-line method double-declining-balance method 20y4 $ $ 20y5 20y6 20y7 total $