The lifespan of a certain brand of light bulb is normally distributed with a mean of 1200 hours and a standard deviation of 80 hours.
Find the probability that a randomly selected light bulb lasts for less than 1050 hours.
An engineer claims that the manufacturing process has changed, causing the mean lifespan to decrease.
State the engineer's null and alternative hypotheses.
A sample of 30 light bulbs is tested and the mean lifespan is found to be 1175 hours.
Carry out a test at the 10% significance level to determine if there is evidence that the mean lifespan is less than 1200 hours.
