Mathematics, 30.03.2021 19:00 kcruz0609

More than 100 million people around the world are not getting enough sleep; the average adult needs between 7.5 and 8 hours of sleep per night. College students are particularly at risk of not getting enough shut-eye. A recent survey of several thousand college students indicated that the total hours of sleep time per night, denoted by the random variable X, can be approximated by a normal model with E(X) = 6.9 hours and SD(X) = 1.21 hours. More than 100 million people around the world are not getting enough sleep; the average adult needs between 7.5 and 8 hours of sleep per night. College students are particularly at risk of not getting enough shut-eye. A recent survey of several thousand college students indicated that the total hours of sleep time per night, denoted by the random variable X, can be approximated by a normal model with E(X) = 6.9 hours and SD(X) = 1.21 hours.
Question 1. Find the probability that the hours of sleep per night for a random sample of 4 college students has a mean x between 6.6 and 6.96. (use 4 decimal places in your answer)
Question 2. Find the probability that the hours of sleep per night for a random sample of 16 college students has a mean x between 6.6 and 6.96 (use 4 decimal places in your answer)
Question 3. Find the probability that the hours of sleep per night for a random sample of 25 college students has a mean x between 6.6 and 6.96. (use 4 decimal places in your answer)
Question 4. The Central Limit Theorem was needed to answer questions 1, 2, and 3 above. True False

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