Instructions: Solve the following problems by applying the Normal distribution 1.- The weight of newborns follows a normal distribution with a mean of 3.5 kg and a standard deviation of 0.5kg. Calculate the probability that a newborn weighs: (a) more than 4kg (b) less than 3.5kg (c) more than 3kg (d) less than 2.5kg.
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!
Instructions: Solve the following problems by applying the Normal distribution
1.- The weight of newborns follows a normal distribution with a
(a) more than 4kg (b) less than 3.5kg (c) more than 3kg (d) less than 2.5kg.
2.- The producer of a certain type of refrigerator indicates that the average life of the refrigerator is 8.7 years under usual conditions. If it is assumed that the life of the refrigerators are
are
a) less than 6 years b) longer than 10 years c) between 4.5 and 7 years
3.- The heights (in metres) of the individuals in a certain population have a mean of 1.69 and a standard deviation of 4.75 if we assume that the behaviour of the population is normal. Calculate the probability that when choosing randomly an individual from the same population, this one presents a height of 1.75m.
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