Part 1) Amount of Sleep A sleep study administered to U.S. adults showed that the amount of sleep (in hours) they get in a 24-hour period is normally distributed with a mean of 6.5 hours and a standard deviation of 1.25 hours. Use normal probability calculations to answer the following questions. Show your calculator functions or Excel commands to receive full credit. Round your answers to 4 decimals. 1. A) How many hours of sleep did you get last night (round to the nearest quarter of an hour)? ____________ B) Ask an adult friend or a family member how many hours of sleep he/she got last night (round to the nearest quarter of an hour). Report below. Make sure it is different than your sleep amount. ____________ 2. What is the probability that a randomly selected U.S. adult slept less than your friend or family member did last night? 3. What is the probability that a randomly selected U.S. adult slept more than you did last night? 4. Doctors recommend 8 hours of sleep per day for adults to have the health benefits of sleep. What percent of U.S. adults sleep less than this recommended amount? 5. A colleague at work says that she usually sleeps less than 4 hours each day. Is her sleep amount unusual? Justify your answer by calculating its probability. 6. 10% of U.S. adults sleep more than how many hours? 7. A simple random sample of 25 U.S. adults is taken. What is the mean and standard deviation of the sampling distribution of sample means? Report your answers using the proper symbols. 8. A simple random sample of 25 U.S. adults is taken. What is the probability that the sample mean hours slept is less than what you slept last night?
Part 1) Amount of Sleep
A sleep study administered to U.S. adults showed that the amount of sleep (in hours) they get in a 24-hour period is
Show your calculator
1.
A) How many hours of sleep did you get last night (round to the nearest quarter of an hour)?
____________
B) Ask an adult friend or a family member how many hours of sleep he/she got last night (round to the nearest quarter of an hour). Report below. Make sure it is different than your sleep amount.
____________
2. What is the probability that a randomly selected U.S. adult slept less than your friend or family member did last night?
3. What is the probability that a randomly selected U.S. adult slept more than you did last night?
4. Doctors recommend 8 hours of sleep per day for adults to have the health benefits of sleep. What percent of U.S. adults sleep less than this recommended amount?
5. A colleague at work says that she usually sleeps less than 4 hours each day. Is her sleep amount unusual? Justify your answer by calculating its probability.
6. 10% of U.S. adults sleep more than how many hours?
7. A simple random sample of 25 U.S. adults is taken. What is the mean and standard deviation of the sampling distribution of sample means? Report your answers using the proper symbols.
8. A simple random sample of 25 U.S. adults is taken. What is the probability that the sample mean hours slept is less than what you slept last night?
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