An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, (a) (5 pts) Find a 96% confidence interval for the population mean of all bulbs produced by this firm. (b) (5 pts) How large a sample is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
Added by Alberto C.
Close
Step 1
04. Divide this by 2 to get 0.02. Look up the z-score for 0.02 in the z-table, which is approximately 2.5. Calculate the margin of error: 2.5 * (40 / sqrt(30)) = 14.96 Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 51 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
a) An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm. b) How large a sample is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
Lien L.
(a) (6 pts.) An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 98% confidence interval for the population mean of all bulbs produced by this firm. (b) (4 pts.) How large a sample is needed in (a) if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
Sri K.
According to the Bureau of Labor Statistics publication News, self-employed persons with home-based businesses work a mean of 25.4 hours per week at home. Assume a standard deviation of 10 hours. a. Identify the population and variable. b. For samples of size $100,$ find the mean and standard deviation of all possible sample mean hours worked per week at home. c. Repeat part (b) for samples of size $1000 .$
The Sampling Distribution of the Sample Mean
The Mean and Standard Deviation of the Sample Mean
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD