Below is a density curve for the distribution of values. Answer the following parts. round to 3 decimal places a. What is the length of the density curve? b. What is the width of the density curve? c. What is the area of the density curve? d. What percentage of the data lies below 1.5 (Hint: use the x-axis)? e. What percentage of the data lies above 0.5? f. What percentage of the data lies between 0.6 and 2.8?
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!
Below is a density curve for the distribution of values. Answer the following parts. round to 3 decimal places
a. What is the length of the density curve?
b. What is the width of the density curve?
c. What is the area of the density curve?
d. What percentage of the data lies below 1.5 (Hint: use the x-axis)?
e. What percentage of the data lies above 0.5?
f. What percentage of the data lies between 0.6 and 2.8?
Observe that the value of the density is positive and equal to 0.25 for values of x between 0 and 4. So, the length of the density curve is the length on x-axis over which the density is positive, which is 4-0=4
(a) So, length of the density curve is 4.
(b) width of the density curve is 0.25, because the shape of density curve is rectangle, and its width is 0.25
(c) Area of the density curve = length * width of rectangle , so , area of the density curve is 4*0.25=1
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