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The following problems reflect the reading material you had to prepare for this week. From the list below, choose one problem, write it down, and solve it in detail (show all of your steps). You should pick a problem that has not yet been attempted if you can. Please label your solution with the corresponding question number. In your solutions, you are only to use the math concepts that have been covered in this course up to this point.
Respond to at least two of your classmates’ posts. Responses to your peers must be substantive and should critique their solutions to help them correct or improve their work. Do not solve the problem for them if they have posted incorrect work. Replies to your professor that are required to correct or clarify your work do not count towards the requirement of two replies. If your professor asks a question directed to the entire class, answers to that question count towards your reply requirement.
You must participate in the forum on at least two days.
Your other replies should attempt to discuss the problem. Here are some suggestions:
a) Discuss what you learned from the problem.
b) Discuss something the problem made you think about.
c) If we were to change the problem slightly, address how the answer would change.
See the syllabus for complete grading information
1. Thousands of fluorescent light bulbs have been made at a factory. It is desired to determine the mean of all the light bulbs. A random sample of 70 fluorescent light bulbs has a mean life of 610 hours. Assume the population standard deviation is 36 hours.
a) Construct a 95% confidence interval for the population mean.
b) To construct the interval in part a, did you use the t-distribution or the standard normal distribution? Explain.
c) Which of the following are we 95% confident is in the confidence interval?
i) The usual amount of time a bulb lasts.
ii) The true population average of all thousands of bulbs of this type.
iii) The sample mean of the 70 bulbs.
d) Explain why a bulb that lasted 620 hours is NOT unusual, even though it is NOT in the confidence interval?
