40 residents on their floor, she determines the values of x and y (in minutes). It obtains the following results: Average age: x = 85 Average time: y = 500 Standard deviation corrected for ages: Sx = 10 Time corrected standard deviation: Sy = 100 Covariance corrected between age and time: Sxy = 750 Determine the average time (in minutes) needed to care for a resident of 80 years old.
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 nurse in charge of the 1st floor of a senior citizen center would like to know if there is a relationship between the age of a resident (x) and the time spent per day in the care of the resident (y). For each of the 40 residents on their floor, she determines the values of x and y (in minutes). It obtains the following results:
Average age: x = 85
Average time: y = 500
Standard deviation corrected for ages: Sx = 10
Time corrected standard deviation: Sy = 100
Determine the average time (in minutes) needed to care for a resident of 80 years old.
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