With this normal distribution problem

900 = 750 + 2*75. In other words, 900 is 2 standard deviations away from the mean. Similarly, 975 is 3 standard deviations from the mean. So

is the random variable for the lifespan of a light bulb with the given normal distribution, and with the standard normal distribution.

We get

If you don't have a calculator/lookup table available, you can invoke the empirical rule, the one that says

The normal distribution is symmetric about its mean, so we also know

Then

0.021

Step-by-step explanation:

One way in which to approach this problem solution is to use a calculator that has statistical distribution functions built in.  My old TI-83Plus has the function "normalcdf," which does the job nicely.

Typing in normalcdf(900,975,750,75) results in the probability 0.021 that a light bulb chosen at random will last between 900 and 975 hours.

Using a table of z-scores would be a good alternative approach.  Note that the z-score corresponding to 750 hours is 0; that for 900 is +2; and that for 975 is +3.  Find the area under the standard normal curve to the left of 975 (z = 3) and that to the left of 900 (z = 2), and then subtract the two results.  It will be 0.021, as before.

25/6

step-by-step explanation:

you multiply 4 by the denominator (4*6=24) and add it to the numerator which makes it 25/6.