MHB What is the probability of exceeding maximum weight with a normal distribution?

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The weight of goats on the farm follows a normal distribution with a mean of 60 kg and a standard deviation of 10 kg. A truck can carry a maximum of 650 kg, and the discussion centers on calculating the probability that the total weight of 10 randomly selected goats exceeds this limit. The sum of the weights of the goats is also normally distributed, which allows for probability calculations using the properties of normal distributions. Participants emphasize the importance of understanding normal distribution and suggest using a normal distribution table for calculations. The conversation highlights the need for clarity on statistical concepts to solve the problem effectively.
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  1. The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds the maximum weight?
 
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Hi secretx

Since you haven't shared any work, we don't know where you're stuck. If you need help with an idea to get you started, note that the random variable that represents the sum of the weights is also a normal distribution because the sum of independent normally distributed variables is also normally distributed (see Wikipedia - Sum of Normally Distributed Variables).
 
Do you know what a "normal distribution" is? Do you have a table of the normal distribution available?
 

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