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The maker of a fitness and sleep tracking app has found that on average, adults tend to sleep less per night than the recommended amount. The app makers have found that the sleep data follows a normal distribution with a population mean (μ) of 6.9 hours sleep per night and a standard deviation (σ) of 1.2 hours. What is the probability that a randomly selected adult will sleep for:

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Less than 5 hours per night

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Between 5 hours and 8 hours per night

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The recommended amount of sleep is 8 hours. In a sample of 3000 adults, find the expected number of people who are getting more than the recommended amount of sleep per night.

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The makers of the app run an advertising campaign on the health benefits of sleep. After the campaign, they find that the standard deviation (σ) has remained the same at 1.2 hours but the percentage of adults sleeping for less than 5 hours per night has fallen to 2.5%. Find the new mean amount of sleep per night.

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The makers of the app run an advertising campaign on the health benefits of sleep. After the campaign, they collected 20 samples and found that the standard deviation (σ) has remained the same at 1.2 hours but the mean number of sleeping hours per night is 7.2 hours. Find a 95% confidence interval for the population mean.

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