Apply the Empirical Rule to solve the following: The weight of a newborn manatee calf is normally distributed with a mean of 66 lbs and a standard deviation of 4 lbs. (Do NOT overuse the calculator on this problem. Apply the Empirical Rule.) a.Draw and label the normal curve. (Don’t forget the word label on the x-axis) b.What percent of manatee calves have a birth weight between 54 and 78 lbs? c. What percent of manatee calves have a birth weight of more than 74 lbs? d .What is the birth weight of the middle 68% of manatee calves? e. What percent of manatee calves weigh more than 58 lbs at birth? f. How much do the smallest 0.15% of manatee calves weigh at birth? g. What percent of manatee calves weigh less than 62 lbs at birth? h. What percent of manatee calves weigh 66 lbs or more at birth?
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!
Apply the
(Do NOT overuse the calculator on this problem. Apply the Empirical Rule.)
a.Draw and label the normal curve. (Don’t forget the word label on the x-axis)
b.What percent of manatee calves have a birth weight between 54 and 78 lbs?
c. What percent of manatee calves have a birth weight of more than 74 lbs?
d .What is the birth weight of the middle 68% of manatee calves?
e. What percent of manatee calves weigh more than 58 lbs at birth?
f. How much do the smallest 0.15% of manatee calves weigh at birth?
g. What percent of manatee calves weigh less than 62 lbs at birth?
h. What percent of manatee calves weigh 66 lbs or more at birth?
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