Question

Understand sampling distributions and the Central Limit Theorem for Means 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 $24,500. Suppose a random sample of 150 Americans is selected. Identify each of the following, rounding your answers to the nearest cent when appropriate: Provide your answer below: u=$ o=$

Answer 1

The information is given as follows: 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 u = $306,500 and a standard deviation o=$24,500. The random sample of n=150 Americans is selected. The central limit theorem is given below: The central limit theorem is used to construct a sampling distribution. 1 The shape of sampling distribution: the sample size is 30 or greater, the distribution of the sample means is approximately normal. 2. Mean of the distribution: The mean of a sampling distribution is the mean of the population, that is, lę = ul. 3. The standard error of the distribution: The standard deviation of a sample mean is equal to the standard deviation of the population divided by the square of the sample size, that is, √n The answers are given below: u = $ 306,500 o = $ 24,500 n=150 Mlp = 306,500 24500 150 = 2000.42 Hence, Os = $2,000.42

Answer 2

solution Given M= population mean = 8306,500 Standard deviation of =&24,500 population n = sample size=150 mean of sauple aurant = f(x) = $306,500 standerd de viation ruarie ८ 24,500 = $20000 4166 Vio 64 ~182000.42