The life expectancy of a typical lightbulb is normally distributed with a mean of 2,000 hours and a standard deviation of 27 hours. What is the probability that a lightbulb will last between 1,975 and 2,050 hours?

A. 0.17619

B. 0.32381

C. 0.79165

D. 0.96784

The first standard deviation covers about 68% of the distribution in a normal curve. (34% higher, 34% lower than the mean). the second standard deviation covers 28% (14% between 1st and 2nd SD above the mean, 14% between 1st and 2nd SD below the mean). In our case

1 Standard deviation = 27 hours (we will approximate to 25 hours)

Mean = 2,000

This means that 34% of the distribution is between 1975 and 2000 hours (within 1 standard deviation below the mean)

2,000 - 2,050 covers the range within 50 hours above the mean.

50 hours is roughly 2 standard deviations. The second standard deviation (standard deviation between 1 and 2) covers around 14% on each side of the distribution.

50 hours is roughly 2 standard deviations, which means we add 34% + 14% = 48%.

The range of 1,975 - 2,050 hours covers 34% of the distribution below the mean and 48% of the distribution above the mean.

This means that the probability that the light bulb will last somewhere within this range is 34% + 48% = 82%

The closest answer is 79%. The difference can be explained by the fact that, for simplicity, we approximated the standard deviation to be ~25 hours instead of the real standard deviation of 27 hours.

0.7916, so it would be c