Question

Based on past​ experience, a bank believes that 1313​% of the people who receive loans will not make payments on time. The bank has recently approved 100100 loans. Answer the following questions. ​a) What are the mean and standard deviation of the proportion of clients in this group who may not make timely​ payments? mu (ModifyingAbove p with caret )μpequals=nothing

Answer 1

Answer:

Mean is 0.13

Standard deviation is 0.0336.

Step-by-step explanation:

For each loan, there are only two possible outcomes. EIther it is paid on time, or it is not. The probability of a loan being paid on time is independent of other loans. So we use the binomial probability distribituon to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The mean of the proportion is given by:

$E(X) = p$

The standard deviation of the proportion is:

$\sqrt{V(X)} = \sqrt{\frac{p(1-p)}{n}}$

In this problem, we have that

$n = 100, p = 0.13$.

Mean

$E(X) = p = 0.13$

Standard deviation

$\sqrt{V(X)} = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.13*0.87}{100}} = 0.0336$