Question

This problem has been solved! See the answer A bank is experimenting with programs to direct bill companies for commercial loans. They are particularly interested in the number of errors of a billing program. To examine a particular program, a simulation of 1000 typical loans is run through the program. The simulation yielded a mean of 4.6 errors with a standard deviation of 0.5. Consturct a 95% confidence interval on the true mean error rate.

Answer 1

Answer: The 95% confidence interval would be (4.57,4.63).

Step-by-step explanation:

Since we have given that

N = 1000 typical loans

Mean = 4.6 errors

Standard deviation = 0.5 errors

At 95% confidence, z = 1.96

So, 95% confidence interval on the true mean error rate is given by

$\mu\pm z\dfrac{\sigma}{\sqrt{N}}\\\\=4.6\pm 1.96\times \dfrac{0.5}{\sqrt{1000}}\\\\=(4.6-0.031,4.6+0.031)\\\\=(4.569,4.631)\\\\=(4.57,4.63)$

Hence, the 95% confidence interval would be (4.57,4.63).