In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead. construct 90% confidence interval for the proportion of water specimens that contain detectable levels of lead.

(0.4958, 0.7422)

Step-by-step explanation:

Let p be the true proportion of water specimens that contain detectable levels of lead. The point estimate for p is . The estimated standard deviation is given by . Because we have a large sample, the 90% confidence interval for p is given by where is the value that satisfies that above this and under the standard normal density there is an area of 0.05. So, the confidence interval is , i.e., (0.4958, 0.7422).

i don't even know man. edge inuity be messing with us. i had to ask a question too.

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.