a. What proportion of female cats have weights between 3.7 and 4.4 kg? b. A certain female cat has a weight that is 0.5 standard above the mean. What proportion of female cats are heavier that this one? c. How heavy is a female cat whose weight is on the 80th percentile? d. A female cat is chosen at random. What is the probability that she weighs more than 4.5 kg?
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!
Weights of female cats of a certain breed are
and standard deviation 0.5 kg.
a. What proportion of female cats have weights between 3.7 and 4.4 kg?
b. A certain female cat has a weight that is 0.5 standard above the mean. What proportion of female
cats are heavier that this one?
c. How heavy is a female cat whose weight is on the 80th percentile?
d. A female cat is chosen at random. What is the probability that she weighs more than 4.5 kg?
e. Six female cats are chosen at random. What is the probability that exactly one of them weights
more than 4.5 kg?
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