Suppose 10 percent of households earn over 80.000 dollars a year, and 0.25 percent of households earn over 450,000. A random sample of 400 households has been chosen. In this sample, let X be the number of households that earn over 80,000, and let Y be the number of households that earn over 450,000. Use normal and Poisson approximation, whichever is appropriate in either case, to find the simplest estimates you can for the probabilities P(X 48) and P(Y 2).

0.1056

0.2642

Step-by-step explanation:

N = 400

P = 10%

n*p = 400*0.1 = 40

n(1-p) = 400 * 0.9 = 360

40 and 360 are greater than 5 so we use the normal distribution here to estimate further.

mean = n*p = 40

sd =

p(X≥48)

= p(X≥47.5)

= 0.8944

1 - 0.8944

= 0.1056

FOR Y

N = 400 p = 0.25% = 0.0025

400 * 0.0025 = 1

1 is less than 5 so we use poisson distribution.

using the excel function,

1 - BINOMDIST(1, 400, 0.0025, TRUE)

= 1 - 0.735759074

= 0.2642

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

the answer for your question is

step-by-step explanation: