**Title: Understanding Sampling Distributions in Loan Repayment****Introduction**Based on past experience, a bank believes that 7% of individuals who receive loans will not make payments on time. The bank has recently approved 200 loans.**Sampling Distribution and Normal Approximation**To approximate the sampling distribution with a normal model, consider the following assumptions:**Assumptions:**- The sample size is sufficiently large.- The probability of success (not making timely payments) is consistent across loans.- Each loan approval is independent of another.**Mean and Standard Deviation Calculation**The next step involves calculating the mean and standard deviation of this model:- **Mean =** [Input box]- **Standard deviation (accurate to 3 decimal places) =** [Input box]**Calculating Probability**Determine the probability that over 10% of these clients will not make timely payments:- [Input box for probability result]**Get Assistance**- For further questions, click on **Question Help** or **Message Instructor**.**Submit Your Answer**After completing the calculations, press the **Submit Question** button to enter your response.---This exercise enhances understanding of the use of normal approximation in real-world scenarios involving sampling distributions, focusing on loan repayment behaviors.

Determine the assumptions that must be true in order to approximate the sampling distribution with normal. The assumptions are determined below as follows: Independence condition: It can be assumed that the all of the loan receivers have been randomly applied and approved by the bank too. 10% condition: It can be assumed that if bank has approved 2000 loans , the sample is less than 10% of the total loan receivers. The value for and are both greater than 5, that is both the conditions are satisfied. Since both conditions are satisfied, this implies that normal approximation is appropriate. Obtain the values of mean and standard deviation. The mean of the sampling distribution is, Thus, the value of mean is 0.07. The standard deviation of the sampling distribution is, Thus, the value of the standard deviation of the model is 0.018.Determine the probability that over 10% of these clients will not make the timely payments. The probability that over 10% of these clients will not make timely payments is obtained below as follows: The required probability is, The probability that over 10% of these clients will not make timely payments is 0.0475.

Math

Statistics

Based on past experience, a bank believes that 7 % of the people who receive loans will not make payments on time. The bank has recently approved 200 loans. What assumptions must be true to be able to approximate the sampling distribution with a normal model? Assumptions: standard What are the mean and standard deviation of this model? mean = deviation (accurate to 3 decimal places) = What is the probability that over 10% of these clients will not make timely payments?

Based on past experience, a bank believes that 7 % of the people who receive loans will not make payments on time. The bank has recently approved 200 loans. What assumptions must be true to be able to approximate the sampling distribution with a normal model? Assumptions: standard What are the mean and standard deviation of this model? mean = deviation (accurate to 3 decimal places) = What is the probability that over 10% of these clients will not make timely payments?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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