Out of 100 days on which the confidence interval happens to be [0.2, 0.3

The length of time a structural element can survive at temperature is a safety critical element of the system. The system requirements state the element must survive 100 C for at least 88 seconds. You collect a sample of 11 experiments measuring the time at temperature to failure of the element. Your sample has a mean of 83 seconds and a standard deviation of 3 seconds. You are constructing a 99% Confidence Interval to verify the requirement.What is the Lower Limit of the Confidence Interval?

Determine the 99% confidence interval for the population mean. (Round your answers to 3 decimal places.)

Construct a 90% confidence interval for 𝜇 if a random sample of size n = 30 results in a sample mean = 45 and s = 2.2. The value of 𝜎 is unknown.

In a survey of 500 college students, 250 of them said they had stayed up late more than 10 times in the past year. A 95% confidence interval is constructed based on the percentage of college students in this sample who stay up late more than 10 times. What is the lower limit for the interval? (round the answer to two decimal places)

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval?