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

(

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4

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≈

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.

0

7

0

2

50

(0.56)(0.44)

≈0.0702.

P(

p

^

p

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

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P(

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>0.6)=P(z>

0.0702

0.6−0.56

)=P(z>0.57)=1−0.7157=0.2843

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