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# Answer to Question #17202 in Statistics and Probability for Kristen

Question #17202
1. The new Twinkle bulb has a standard deviation hours. A random sample of 60 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,  of all Twinkle bulbs.

2. A standard placement test has a mean of 125 and a standard deviation of  = 15. Determine the minimum sample size if we want to be 90% 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 20 randomly selected eggs and found that the mean amount of cholesterol was 180 mg. The sample standard deviation was found to be s = 25.0 mg on this group. Assume that the population is normally distributed.

a. Find the margin of error for a 95% confidence interval. Round your answer to the nearest tenths.

b. Find a 95% confidence interval for the 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 120 of these new bulbs is selected from the production line. It was found that 90 lasted more than 1000 hours.

a. Construct a 99% confidence interval for the population proportion “p” of all Twinkle bulbs. Round to the nearest three decimals.

b. Construct a 95% confidence interval for the population proportion “p” of all Twinkle bulbs. Round to the nearest three decimals.
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