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

(

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>

0

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6

)

=

P

(

z

>

0

.

6

−

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5

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0

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=

P

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1

5

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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

idk

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.