SOLUTION: Hi Any help you can give me on these problems will be greatly appreciated. 1) The new Twinkle bulb has a standard deviation 35 hours. A random sample of 50 light bulbs is sele

Question 444206: Hi
Any help you can give me on these problems will be greatly appreciated.
1)
The new Twinkle bulb has a standard deviation 35 hours. A random sample of 50 light bulbs is selected from inventory. The sample mean was found to be 500 hours.
(a. Find the margin of error E for a 95% confidence interval. Round your answer to the nearest hundredths.
(b. Construct a 95% confidence interval for the mean life, mu of all Twinkle bulbs.
2) A standard placement test has a mean of 115 and a standard deviation of  = 10. Determine the minimum sample size if we want to be 95% certain that we are within 3 points of the true mean.
3)An experimental egg farm is raising chickens to produce low cholesterol eggs. A lab tested 16 randomly selected eggs and found that the mean cholesterol was 190 mg with a standard deviation of 18.0 mg. Assume that the population is normally distributed.
a. What is the margin of error for a 95% confidence interval? Round your answer to the nearest tenths.
b. What is the 95% confidence interval for the population mean cholesterol content for all experimental eggs? Assume that the population is normally distributed.
4. The new Twinkle bulb is being developed to last more than 1000 hours. A random sample of 100 of these new bulbs is selected from the production line. It was found that 64 lasted more than 1000 hours.
a. What is the margin of error (E)? Round to the nearest three decimals.
b. What is the 95% confidence interval for the population proportion (p) of all Twinkle bulbs?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Any help you can give me on these problems will be greatly appreciated.
---------
All of your problems are essentially the same.
You need a "sample mean"(x-bar) and you need a "margin of error"(ME).
The sample mean is provided by the problem narrative.
The ME = z*s/sqrt(n) where z depends on the level of confidence,
s is the standeard deviation (usually given) and n is the sample size.
The Confidence Interval is (x-bar - ME) < u < (x-bar + ME)
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1)
The new Twinkle bulb has a standard deviation 35 hours. A random sample of 50 light bulbs is selected from inventory. The sample mean was found to be 500 hours.
(a. Find the margin of error E for a 95% confidence interval. Round your answer to the nearest hundredths.
ME = z*s/sqrt(n)
ME = 1.96*35/sqrt(50) = 9.7015
=====================================
(b. Construct a 95% confidence interval for the mean life, mu of all Twinkle bulbs.
500-9.7015 < u < 500+9.7015
===================================
Cheers,
Stan H.

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