let p(x) 1 2x, q(x) x x2 , and r(x) 2 3x x2 . Determine whether s(x) is in span(p(x), q(x), r(x)). 54. s(x) 1 x x2

Homework 5 Explanations Stat To find the probability of a shaded region, use normalcdf(a,b,μ,σ) - (number given, 10, 0,1) - 10 is used because is it big enough to cover all outcomes Finding the probability that X falls within a certain amount of the μ is found by using normalcdf(number given, 10, 0, 1)-normalcdf(10, number given, 0, 1) Definition of binomial- x is account for the number of trials of an independent random variable. - As the number changes, binomials are no longer reliable, as with drawing marbles out of a bag and not replacing them. Finding z scores for which a total probability of 0.39 falls more than z standard deviations in either direction from the mean - 0.39 is the outside of both z-scores; 1-0.39=0.61 is the area inside the two z scores; 0.39/2=0.195; 0.195+0.61=0.805 which is the area of z to the left or -z to the right - z=inversenorm(.805)=0.86 - μ + zσ is in the 80.5th percentile because 80.5% of the population falls below the standard deviation or 19.5% of the population falls above the standard deviation Finding z scores for which the probability falls within a probability of μ - 0.36 inside both z scores; 1-0.36=0.64 outside the z scores - ½(0.64)= 0.32 outside each side +0.36= 0.68 which is to the left or right of a z score - z=inversenorm(0.68)=0.47 inside z scores Finding the greater than proportion - μ = 682