Q.A sample of 100 invoices from a firm's ledger has a mean value of Rs. 150 (in hundreds) with a known population standard deviation of Rs. 25 (in hundreds). Construct a 95% confidence interval for the true population mean invoice value.

A point estimate of Rs. 150 (hundred) alone says nothing about its precision, so an interval is built around it using the standard error and the Z-value for 95% confidence. …

Given: $\bar{x} = 150$, $\sigma = 25$, $n = 100$, confidence level = 95% $\Rightarrow Z_{\alpha/2} = 1.96$.

Step 1 - standard error:

Step 2 - margin of error:

Step 3 - confidence interval:

$\bar{x} \pm 4.9 = 150 \pm 4.9 = (145.1,\ 154.9)$ …

Using the wrong Z-value (e.g., 1.645, which is for 90% confidence) is the most frequent error — always match the Z-value to the stated confidence level. Also remember the …