Every year at the AP Statistics Exam reading apparel is sold to commemorate the event. Based on historical data, we know that 56% of teachers will make an apparel purchase. This year, the organizers have decided to select a random sample of 50 teachers. If a selected teacher made an apparel purchase, they will be given a prize. What is the probability that more than 60% of the selected teachers will win a prize

0.284

Step-by-step explanation:

To carry out this calculation, we begin by describing the sampling distribution of the sample proportion.

The sample size is n = 50 and the population proportion of teachers who made an apparel purchase is 0.56.

Shape: Because np = (50)(0.56) = 28 and n(1 – p) = (50)(0.44) = 22 are both at least 10, the shape of the sampling distribution of the sample proportion is approximately Normal.

Center:

μ

p

^

=

p

=

0

.

5

6

μ

p

^

=p=0.56

Variability: The standard deviation of the sample proportion is approximately

(

0

.

5

6

)

(

0

.

4

4

)

5

0

≈

0

.

0

7

0

2

50

(0.56)(0.44)

≈0.0702.

P(

p

^

p

^

> 0.6) = Normalcdf(lower: 0.6, upper: 1000, mean: 0.56, SD: 0.0702) = 0.284.

P

(

p

^

>

0

.

6

)

=

P

(

z

>

0

.

6

−

0

.

5

6

0

.

0

7

0

2

)

=

P

(

z

>

0

.

5

7

)

=

1

−

0

.

7

1

5

7

=

0

.

2

8

4

3

P(

p

^

>0.6)=P(z>

0.0702

0.6−0.56

)=P(z>0.57)=1−0.7157=0.2843

8(-10x+3.5y-7)

8×-10x + 8×3.5y + 8×-7

-80x + 28y - 56

therefore

-80x+28y-56 is the correct answer

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