Answer:
The 95% confidence interval for true mean error is (4.57, 4.63).
Step-by-step explanation:
Let <em>X</em> = the number of errors of a billing program.
According to the Central limit theorem if a large sample (<em>n</em> > 30) is drawn from an unknown population then the sampling distribution of the sample mean will follow a Normal distribution with mean () and standard deviation (
).
The sample size of the loans is, <em>n</em> = 1000.
The mean is, .
The standard deviation is,
The confidence interval for mean is:
The critical value of <em>z</em> for 95% confidence interval is:
**Use the <em>z</em>-table for critical values.
Compute the 95% confidence interval for true mean error as follows:
Thus, the 95% confidence interval for true mean error is (4.57, 4.63).