A particular fruit's weights are normally distributed, with a mean of 204 grams and a standard deviation of 16 grams. If you pick one fruit at random, what is the probability that it will weigh between 167 grams and 247 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!
![**Problem Statement:**
A particular fruit’s weights are normally distributed, with a mean of 204 grams and a standard deviation of 16 grams.
**Question:**
If you pick one fruit at random, what is the probability that it will weigh between 167 grams and 247 grams?
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**Notes for Educational Website:**
The problem describes a scenario involving a normally distributed variable, emphasizing understanding of normal distribution characteristics, including mean and standard deviation. It also highlights the concept of probability within a specific range of a normal distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d67c36c-7658-48f7-9c6c-f8baffcd3897%2F7939e06c-8784-42fe-bd74-a8328579bbc0%2F71nyqsr_processed.jpeg&w=3840&q=75)
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