5.14 Total sleep time of college students. The total sleep time per night among college students was approximately Normally distributed with mean ? = 6.78 hours and standard deviation ? = 1.24 hours. You plan to take an SRS of size n = 150 and compute the average total sleep time. (a) What is the standard deviation for the average time? (b) Use the 95 part of the 68–95–99.7 rule to describe the variability of this sample mean. (c) What is the probability that your average will be below 6.9 hours?
Added by Jeffrey L.
Close
Step 1
So, σ/√n = 1.24/√150 = 0.101. (b) The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 69 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
5.28 - Total Sleep Time of College Students In example, 5.4, the total sleep time per night among college students was approximately normally distributed with a mean = 6.78 hours and standard deviation = 1.24 hours. You plan to take an SRS of size n=120 and compute the average total sleep time. a. What is the standard deviation for the average time? b. Use the 95 part of the 68-95-99.7 rule to describe the variability of this sample mean. c. What is the probability that your average will be below 6.9 hours?
David N.
In a recent survey, the total sleep time per night among college students was approximately Normally distributed with mean μ = 6.76 hours and standard deviation σ = 1.24 hours. You plan to take an SRS of size n = 140 and compute the average total sleep time. (a) What is the standard deviation for the average time? (Round your answer to three decimal places.) (b) Use the 95 part of the 68–95–99.7 rule to describe the variability of this sample mean. (Round your answers to three decimal places.) 95% of the time, we'll expect the sample mean to be between a lower value of and an upper value of hours. (c) What is the probability that your average will be below 6.9 hours? (Round your answer to four decimal places.)
Ahmet Y.
A study being done on college students found that the mean amount of sleep that a college student receives per night is 6.7 hours with a standard deviation of 1.5 hours. Suppose a random sample of 40 college students is taken. Find the probability that the mean amount of sleep will be between 6.5 and 7.0 hours. Round your standard deviation to two decimal places.
Sanchit J.
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