Question

Osmar Ltd conducted a study to determine the lifetimes of the light bulbs produced by their Melbourne plant. Based on studies in other plants, it could be assumed that the variance of the lifetimes was 100000 hours squared. Experimental testing of 50 light bulbs yielded an average lifetime of 27.7 hundred hours. Construct a 90% confidence interval for the average lifetime of the bulbs produced in Osmar's Melbourne plant. Report the lower limit in hours to 1 decimal place.

Answer 1

Let X is a random variable shows the lifetime of bulb. Here X has normal distribution with parameters as follows:

For 90% confidence interval, using excel function "=NORMSINV(0.95)", critical value of z is . So required confidence interval is

Therefore, a 90% confidence interval forthe average lifetime of the bulbs produced in Osmar's Melbourne plant is (-45.9 hour, 101.3 hour).

Lower limit: -45.9 hours