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Tems11 [23]
3 years ago
9

An article in an educational journal discussing a non-conventional high school reading program reports a 95% confidence interval

of (520 , 560) for the average score on the reading portion of the SAT. The study was based on a random sample of 20 students and it was assumed that SAT scores would be approximately normally distributed. Determine the margin of error associated with this confidence interval.
Mathematics
1 answer:
Maksim231197 [3]3 years ago
6 0

Answer:

The margin of error associated with this confidence interval is 20

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound. The interval is symmetric, which means that the margin of error is the difference between these two bounds(upper - lower), divided by 2.

In this problem, we have that:

Lower bound: 520

Upper bound: 560

Determine the margin of error associated with this confidence interval.

(560 - 520)/2 = 20

The margin of error associated with this confidence interval is 20

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Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

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A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

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∴  A ∩ (A' ∪ B) = A ∩ B

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Therefore, (A ∩ A') ∩ B' = ∅  ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.

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