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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.
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answered4 years ago
Explain Bot
answered1 year ago
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.