An experiment was conducted to determine the effects of elapsed time on a person's memory. Subjects were asked to look at a picture which contained many different objects. After studying the pictures, they were asked to recall as so many of the objects as they could. At different time intervals following this, they would be asked to recall as many objects as they could. Based on the experiment, the following function was developed: = f(t) = 90 - 30 ln(t) where t ≥ 1 For this function represents the average percent recall as a function of time since studying the pictures (measured in hours). A value of = 50 would indicate that at the corresponding time t the average recall for the study group was 50 percent. a) What is the average percent recall after 1 hour? b) Find the expression for the rate of change in with respect to time. c) What is the maximum percent and minimum percent recall?
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!
An experiment was conducted to determine the effects of elapsed time on a
person's memory. Subjects were asked to look at a picture which contained
many different objects. After studying the pictures, they were asked to recall as
so many of the objects as they could. At different time intervals following this,
they would be asked to recall as many objects as they could. Based on the
experiment, the following function was developed:
= f(t) = 90 - 30 ln(t) where t ≥ 1
For this function represents the average percent recall as a function of time
since studying the pictures (measured in hours). A value of = 50 would
indicate that at the corresponding time t the average recall for the study group
was 50 percent.
a) What is the average percent recall after 1 hour?
b) Find the expression for the rate of change in with respect to time.
c) What is the maximum percent and minimum percent recall?
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