A particular fruit's weights are normally distributed, with a mean of 463 grams and a standard deviation of 38 grams. If you pick one fruit at random, what is the probability that it will weigh between 360 grams and 384 grams?
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!
A particular fruit's weights are
If you pick one fruit at random, what is the probability that it will weigh between 360 grams and 384 grams? Round to three decimal places.
We have given that,
A normal distribution with mean= 463 and standard deviation = 38.
Here,
From the problem, we need to find out that,
P( 360 < X < 384 ).
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