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.

The 95% confidence interval for true mean error is (4.57, 4.63).

Step-by-step explanation:

Let X = the number of errors of a billing program.

According to the Central limit theorem if a large sample (n > 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, n = 1000.

The mean is, .

The standard deviation is,  

The confidence interval for mean is:

The critical value of z for 95% confidence interval is:

**Use the z-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).

step-by-step explanation:

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