Based on past experience, a bank believes that 6% of the people who receive loans will not make payments on time.The bank has recently approved 300 loans.What is the standard deviation of the proportion of clients in this group who may not make timely payments?
A) $\sigma = 1.88 \%$
B) $\sigma = 1.41 \%$
C) $\sigma = 1.37 \%$
D) $\sigma = 4.11 \%$
E) $\sigma = 4.24 \%$

Question

Based on past experience, a bank believes that 6% of the people who receive loans will not make payments on time.The bank has recently approved 300 loans.What is the standard deviation of the proportion of clients in this group who may not make timely payments? 
A) $\sigma = 1.88 \%$
B) $\sigma = 1.41 \%$
C) $\sigma = 1.37 \%$
D) $\sigma = 4.11 \%$
E) $\sigma = 4.24 \%$

Quizplus · Accepted Answer

The standard deviation of the proportion of clients in this group who may not make timely payments is:$\sigma = \sqrt{p(1-p)/n}$where:p is the proportion of clients who do not make timely payments (0.06)n is the number of loans (300)Plugging in these values, we get:$\sigma = \sqrt{0.06(1-0.06)/300} = 0.0137$or 1.37%

Based on Past Experience, a Bank Believes That 6% of the People