The results of a national survey showed that on average, adults sleep 6.9 hours per night.Suppose that the standard deviation is 1.2 hours and that the number of hours of sleep followsa bell-shaped distribution.a. Use the empirical rule to calculate the percentage of individuals who sleep between4.5 and 9.3 hours per day.b. What is the z-value for an adult who sleeps 8 hours per night?c. What is the z-value for an adult who sleeps 6 hours per night?
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!
The results of a national survey showed that on average, adults sleep 6.9 hours per night.
Suppose that the standard deviation is 1.2 hours and that the number of hours of sleep follows
a bell-shaped distribution.
a. Use the
4.5 and 9.3 hours per day.
b. What is the z-value for an adult who sleeps 8 hours per night?
c. What is the z-value for an adult who sleeps 6 hours per night?
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