he mean daily production of a herd of cows is assumed to be normally distributed with a mean of 39 liters, and standard deviation of 2.4 liters. Let X be the production of a randomly selected cow in liters. Please show the following answers to 4 decimal places. If a cow is randomly chosen, find the probability that its production is more than 35.4 liters. If a cow is randomly chosen, find the probability that its production is between 37.8 and 41.4 liters. Please show the following answer to 1 decimal place. The 60th percentile of the milk production is how many liters?
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!
The mean daily production of a herd of cows is assumed to be
Please show the following answers to 4 decimal places.
- If a cow is randomly chosen, find the probability that its production is more than 35.4 liters.
- If a cow is randomly chosen, find the probability that its production is between 37.8 and 41.4 liters.
Please show the following answer to 1 decimal place.
- The 60th percentile of the milk production is how many liters?
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