The weight of packages that are sent by a certain parcel delivery service has a normal distribution with a mean of 12 pounds and a standard deviation of 3.5 pounds. The administration wants to establish a weight c beyond which there will be a premium. This value c will correspond to the one that groups the lower 99% of the parcel, therefore, this value is: a) 21.03 b) 3.85 c) 2.98 d) 20.14
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!
1. The weight of packages that are sent by a certain parcel delivery service has a
a) 21.03
b) 3.85
c) 2.98
d) 20.14
2. The height of Colombian men is 170cm with a standard deviation of 3cm. In a random sample of 4 Colombian men, the probability that two of them are taller than 180cm is:
a) 0.9982
b) 0.9995
c) 1.1036E-6
d) 4.2906E-4
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