The National Sleep Foundation recommends that adults between 18−6418-64 years of age sleep between 77 and 99 hours per night. A researcher collected data on the amount of sleep that students in college slept per night. The data were approximately normally distributed with the following mean and standard deviation mean = 6.86.8 hours standard deviation = 1.81.8 hours
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
| z-Scores and Area under the Curve |
| The National Sleep Foundation recommends that adults between 18−6418-64 years of age sleep between 77 and 99 hours per night. A researcher collected data on the amount of sleep that students in college slept per night. The data were approximately mean = 6.86.8 hours standard deviation = 1.81.8 hours Use this information and the online normal distribution calculator to answer the questions below. Round your percents to two decimal places. Note: Use z-scores rounded to two decimal places and the standard normal distribution to avoid roundoff errors. |
| Normal Calculator |
| What percent of students slept between 77 hours and 88 hours? % |
| What percent of students slept less than 7.37.3 hours? % |
| What percent of students slept more than 9.39.3 hours? % |
| What percent of students slept less than 2.782.78 hours or more than 11.4811.48 hours ? % |
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