A General Electric soft white 3-way bulb has an average life of 1200 hours with a standard deviation of 50 hours. Find the probability that the life of one of these bulbs will be between 1150 and 1300 hours.
You need to change the times to Z-scores — scores given in terms of standard deviations.
Z = (X - µ)/SD, where X is the particular value, µ = the mean and SD is the standard deviation.
Once the Z scores are obtained, look it up in a table in the back of your statistics textbook called something like "areas under the normal distribution." Find the proportions between those Z-scores and the mean for both values and add them together to get the probability that the life of the bulb will be between these two values.
Although I did not solve the problem completely for you, I did tell you the process for reaching a solution. This will mean that you will have to exert a little more effort, time and thinking, but I hope it will help you to learn more.
I hope this helps. Thanks for asking.
did you get the answer now?
To find the probability that the life of the bulb will be between 1150 and 1300 hours, we need to calculate the Z-scores for both values using the formula:
Z = (X - µ) / SD
where X is the particular value, µ is the mean, and SD is the standard deviation.
For 1150 hours:
Z1 = (1150 - 1200) / 50 = -1
For 1300 hours:
Z2 = (1300 - 1200) / 50 = 2
Now we need to look up the proportions between these Z-scores and the mean in a table called the "areas under the normal distribution." This table provides the probabilities of values occurring within specific Z-scores.
Once you find the Z-scores in the table, you can look up the corresponding probabilities. Add these probabilities together to get the final probability.
Although I have explained the process, you will need to refer to your statistics textbook or an online resource with the "areas under the normal distribution" table to complete the calculation.
I hope this clarifies the steps involved.