Question

A bank is reviewing its risk management policies with regards to mortgages. To minimize the risk of lending, the bank wants to compare the typical mortgage owed by their clients against other homebuyers. The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500. Suppose a random sample of 150 Americans is selected. Identify each of the following, rounding your answers to the nearest cent when appropriate:

Answer 1

1. μ = 306,500

2.σ = 24,500

3. n = 150

4. μ$_x$ = $306,500

5. σ$_x$ = $2000

What is Standard deviation?

The standard deviation serves as a gauge for the degree of variation or dispersion among a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.

With a standard deviation of $24,500 and an average mortgage debt of $306,500, Americans have a median mortgage debt.

According to the given information:

The population's average is

μ = 306,500

Standard deviation for the general population is

σ = 24500

Imagine 150 Americans are chosen at random for the sample.

n= 150

The sample mean is roughly normally distributed as a result of the high sample size, which is supported by the central limit theorem.

The population mean and sample mean would be the same,

μ$_n$ = μ =306,500

Here is how to calculate the sample standard deviation:

$\sigma_{x}=\frac{\sigma}{\sqrt{n}}$

the sample size is n, and is the population standard deviation.

$\begin{aligned}&\sigma_{x}=\frac{24,500}{\sqrt{150}} \\&\sigma_{x}=\ 2,000\end{aligned}$

The necessary conditions are thus:

1. μ = 306,500

2.σ = 24,500

3. n = 150

4. μ$_x$ = $306,500

5. σ$_x$ = $2000

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I understand that the question you are looking for is :

A bank is reviewing its risk management policies with regards to mortgages. To minimize the risk of lending, the bank wants to compare the typical mortgage owed by their clients against other homebuyers. The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500. Suppose a random sample of 150 Americans is selected. Identify each of the following, rounding your answers to the nearest cent when appropriate:

1.$1. mu=?\\2. sigma=?\\3. =n= \\4. mu_{overlinex}= x=?\\5. sigma_{overlinex}= x=?$