In this problem, the mean and standard deviation are 7.6 and 0.75 (hours), respectively. We first need to find the z-score for 8.5 hours. This is obtained by doing the subtraction (8.5 - 7.6), which is how many hours above the mean 8.5 hours is, which is 0.9. Then divide by the standard deviation 0.75 to get 1.2 standard deviations above the mean. Then use a normal distribution calculator or a standard normal table to get a proportion of 0.8849 at 1.2 or below. But it's asking for the area to the right of 1.2, which is 1 - 0.8849 = 0.1151.
Emily G.
asked 09/27/19College students average 7.6 hours of sleep per night with a standard deviation of 45 minutes
If the amount of sleep is normally distributed, what proportion of college students sleep for more than 8.5 hours? Round to 4 decimal places.
Probability =
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