In: Math
The lifetime of lightbulbs that are advertised to last for 3900 hours are normally distributed with a mean of 4100 hours and a standard deviation of 300 hours. What is the probability that a bulb lasts longer than the advertised figure?
Given that the distribution is normal with mean=4100 and a standard deviation of 300 hence the probability will be calculated using the Z score and Z table shown below.
Thus Z score at X=3900 is calculated as:
Hence the probability that it last more than advertised is P(X>3900) =P(Z>0.67) which is computed using Z table shown below as:
P(Z>0.67)=1-0.7486
=0.2564