Question

A small micro-loan bank has 1000 loan customers. If the total annual loan repayments made by an individual is a random variable with mean $850 and standard deviation $900, approximate the probability that the average total annual repayments made across all customers is greater than $865.

Answer 1

Solution :

Given that,

mean = = $850

standard deviation = =$900

n=100

= =$850

= / n = 900 / 1000 = 28.4605

P( >$865 ) = 1 - P( < 865)

= 1 - P[( - ) / < (865-850) / 28.4605]

= 1 - P(z <0.53 )

Using z table

= 1 - 0.7019

= 0.2981

probability= 0.2981