Amarket research firm conducts telephone surveys with a 41% historical response rate. a. what is the probability that in a new sample of 400 telephone numbers, at least 135 individuals will cooperate and respond to the questions? in other words, what is the probability that the sample proportion will be at least 135/400 = 0.3375?

probability  is 0.778

Step-by-step explanation:

Given data in question

success of probability (p) = 41% = 0.41

no of sample (n)  = 400

individual = 150

to find out

probability that the sample proportion will be at least 135/400

solution

first we calculate the mean i.e

mean = p × n

mean = 400 × 0.41

mean = 164

now we calculate standard deviation =

standard deviation =  9.83666

we know P(X ≥ 135) = P(Z ≥ (150 - 164)/9.83666)

P(X ≥ 135) = P(Z ≥ (-1.42324)

from table 1 find corresponding probability

P(X ≥ 135) = 1 - P(Z ≥ (-1.42324)

= 1 - 0.9222 = 0.778

probability  is 0.778

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

nada

step-by-step explanation: