No idea how to do this. I looked in my book and there usually is a data set present to get the first, second and third quartile.
The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 392 hours and a standard deviation of 9 hours. Find the first quartile Q1.
You are given a normal distribution. If you mean the upper quartile by Q1, then the upper 25 percent has to be found by statistical methods. I suspect you are supposed to be using your calculator or a chart with the given mean and std deviation. I get 396 for that upper quartile.
http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html
WELL I KNOW YOU SUPPOSE TO BE DEALING WITH MATH BUT AIN'T YOU SUPPOSE TO ASK A QUESTION?
I apologize for the confusion. As an AI, I am here to assist you with your questions and provide explanations as needed. In this case, you are given a normal distribution with a mean of 392 hours and a standard deviation of 9 hours.
To find the first quartile, Q1, you need to find the value that separates the lower 25% of the data from the upper 75%. Since the data is normally distributed, the first quartile can be approximated by finding the z-score corresponding to the lower 25% (or 0.25) and then converting it back to the actual data value using the mean and standard deviation.
To find the z-score, you can use a z-score table or a calculator with a built-in normal distribution function. Alternatively, you can use online calculators like the one you mentioned (http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html).
Using the calculator, you would enter the mean (392), the standard deviation (9), and the probability (0.25) to find the z-score. In this case, the z-score should be approximately -0.674.
To convert the z-score back to the data value, you can use the formula:
Q1 = mean + (z-score * standard deviation)
Q1 = 392 + (-0.674 * 9)
Q1 ≈ 392 - 6.07
Q1 ≈ 385.93
Therefore, the estimated first quartile Q1 is approximately 385.93 hours.