SOLUTION: The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 75 hours. A random sample of 36 li
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Question 1120034: The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 75 hours. A random sample of 36 light bulbs indicated a sample mean life of 260 hours. Complete parts (a) through (d) below.
a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment.
The 95% confidence interval estimate is from a lower limit of
nothing hours to an upper limit of
nothing hours.
(Round to one decimal place as needed.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the 95% confidence interval requires a critical z-score of plus or minus 1.959963986.
the z-score formula is:
z = (x - m) / s
z is the z-score.
x is the raw score.
m is the raw mean.
s is the standard error.
your raw mean is 260 hours.
your population standard deviation is 75 hours.
your sample size is 36.
formula for standard error is:
standard error = standard deviation / square root of size.
in your problem, you get:
s = 75 / sqrt(36) = 75 / 6 = 12.5.
use the critical z-scores and the standard error and the mean to find the critical raw scores.
formula is z = (x - m) / s
z = plus or minus 1.959963986.
s = 12.5
on the low side, the z-score formula becomes:
-1.959963986 = (x - 260) / 12.5
solve for x to get x = 235.5004502
on the high side, the z-score formula becomes:
1.959963986 = (x - 260) / 12.5
solve for x to get x = 284.4995498.
that's your 95% confidence interval.
following is a picture of the 95% confidence interval using z-scores.
following is a picture of the 95% confidence interval using raw scores.
in both, the area under the normal distribution curve is shown as .95.
that's the same as 95%.
your confidence interval is the shaded area on the graph.
the critical z-score was found using the inverse norm function of the TI-84 Plus calculator.
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