To solve this problem, we can model the situation using a binomial distribution since we are dealing with a fixed number of trials (loans), each with two possible outcomes (making payments on time or not).
Let:
- \( n \) = number of trials (loans approved) = 200
- \( p \) = probability of success (not making payments on time) = 0.08
- \( q \) = probability of failure (making payments on time) = \( 1 - p = 0.92 \)
Mean
The mean \( \mu \) of a binomial distribution can be calculated using the formula:
\[ \mu = n \cdot p \]
Substituting in the values:
\[ \mu = 200 \cdot 0.08 = 16 \]
Standard Deviation
The standard deviation \( \sigma \) of a binomial distribution can be calculated using the formula:
\[ \sigma = \sqrt{n \cdot p \cdot q} \]
Substituting in the values:
\[ \sigma = \sqrt{200 \cdot 0.08 \cdot 0.92} \] \[ \sigma = \sqrt{200 \cdot 0.0736} \approx \sqrt{14.72} \approx 3.84 \]
Conclusion
Thus, the mean number of people who will not make payments on time is \( 16 \), and the standard deviation is approximately \( 3.84 \).
9 answers