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lara31 [8.8K]
3 years ago
11

A random sample of 144 observations produced a sample proportion of 0.4. An approximate 90% confidence interval for the populati

on proportion p is between:_______
a) 0.320 and 0.480
b) 0.333 and 0.480
c) 0.333 and 0.467
d) 0.359 and 0.441
e) 0.313 and 0.487
Mathematics
1 answer:
EleoNora [17]3 years ago
7 0

Answer:

CI =(0.333, 0.480)

Step-by-step explanation:

The formula for calculating the confidence interval is expressed as shown;

CI = p±Z * √p(1-p)/n±0.5/n

Z is the z-score at 90% confidence

p is the sample proportion

n is the sample size

Given n = 144, p = 0.4 and z-score at 90%  CI = 1.645 (from z table)

Substituting this values;

CI = p ± 1.645*√0.4(1-0.4)/144 ±0.5/n

CI = 0.4 ± 1.645*√0.4(0.6)/144 ± 0.5/144

CI = 0.4 ±1.645 * √0.24/144 ± 0.00347

CI = 0.4 ±1.645 * 0.04087± 0.00347

CI = 0.4±0.06723±0.00347

CI =(0.333, 0.480)

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Help me why is it this answer? How do i solve that type of math problem green is the answer ​
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Answer:

To increase a price, add the percentage you wish to increase it by to 100%, convert the percentage into a decimal by dividing by 100, then multiply this by the original price.

To decrease a price, subtract the percentage you wish to decrease it by from 100%, convert the percentage into a decimal by dividing by 100, then multiply this by the original price.

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100% represents the original price.

Therefore, 100% = $599.99

A 20% discount means that the price is now 80% of the original price,
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To find 80% of the original price, convert 80% to a decimal and multiply it by the original price:

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Therefore, 80% of $599.99 = 0.8 x $599.99

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Finally, we need to apply a sales tax of 6%.  We can do this in 2 ways:

<u>Way 1</u>

Work out 6% of the discounted price, then add this to the discounted price to find the final price:

Sales tax = 6% of $479.992

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               = $28.79952

Final price = discounted price + sales tax

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<u>Way 2</u>

We need to increase the discounted price of $479.992 by 6%.  Therefore, the final price will be 106% of the discounted price as
100% + 6% = 106%

Final price = 106% of discounted price

                  = 1.06 x $479.992

                  = $508.79 (nearest cent)

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2 years ago
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