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3 years ago

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When she graduates college Linda will owe 43,000 in student loans. The interest rate on the federal Liana is 4.5 % and the rate

on the private is 2%. The total interest she owes for one year was 1,585. What is the amount of each loan

1 answer:

Amanda [17]3 years ago

6 0

Answer:

federal loan amount = $29,000

private loan amount = $14,000

Step-by-step explanation:

Total amount is 43000

Let amount in federal be f

and

amount in private be 43,000 - f

Interest rate at federal is 0.045

Interest rate at private is 0.02

THus, we can form the equation shown below and solve:

f(0.045) + (43,000 - f)(0.02) = 1585

0.045f +860 - 0.02f = 1585

0.025f = 725

f = 29,000

and on private = 43,000 - 29,000 = 14,000

Hence

federal loan amount = $29,000

private loan amount = $14,000

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To solve this problem, it is important to know the normal probability distribution and the central limit theorem.

Normal probability distribution

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In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 11, \sigma = 3$

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 25, s = \frac{3}{\sqrt{25}} = 0.6$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

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$Z = \frac{10.8 - 11}{0.6}$

$Z = -0.33$

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Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

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$Z = \frac{11 - 11}{0.6}$

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