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LiRa [457]
11 months ago
8

SOCIAL SECURITY Social Security numbers are of the form XYZ - MN - ABCD. A. The first three digits XYZ are referred to as the ar

ea number. The number is associated with where you registered for your social security card. X is a number 1-7. Y and Z can be any number 0-9. Also the area code 666 has never been used. How many area code numbers are possible? 10SHOW YOUR WORK
Mathematics
1 answer:
aev [14]11 months ago
6 0

Social Security numbers are of the form XYZ - MN - ABCD

Part A:

The first three digits XYZ are referred to as the area number

X is a number 1 - 7 (1, 2, 3, 4, 5, 6, 7)

That means we have 7 choices for X

Y and Z can be any number 0 - 9 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

That means we have 10 choices for Y and also 10 choices for Z

So, the number of possible ways are

7\times10\times10=700

But we know that the area code 666 has never been used.

So we need to subtract this one from the total.

700-1=699

Therefore, the total number of possible area codes is 699.

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In this problem, we have a 98% confidence level, hence\alpha = 0.98, z is the value of Z that has a p-value of \frac{1+0.98}{2} = 0.99, so the critical value is z = 2.327.

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M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.02 = 2.327\sqrt{\frac{0.5(0.5)}{n}}

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\sqrt{n} = \left(\frac{2.327 \times 0.5}{0.02}\right)

(\sqrt{n})^2 = \left(\frac{2.327 \times 0.5}{0.02}\right)^2

n = 3,385.

A sample size of 3,385 is required.

More can be learned about the z-distribution at brainly.com/question/25890103

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