Statistics and probability

In summary, the weight of goats at a farm follows a normal distribution with a mean of 60 kg and a standard deviation of 10 kg. The maximum weight that a truck can accommodate is 650 kg. To find the probability of the total weight exceeding the maximum weight, we can use the normal distribution table and the fact that the sum of independent normally distributed variables is also normally distributed.
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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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  • #2
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).
 
  • #3
Do you know what a "normal distribution" is? Do you have a table of the normal distribution available?
 

1. What is the difference between statistics and probability?

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves techniques for summarizing and describing data, as well as making inferences and predictions based on the data. Probability, on the other hand, is the branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is used to quantify the uncertainty of outcomes in various situations.

2. Why is it important to understand statistics and probability?

Statistics and probability are important because they help us make sense of the world around us. They allow us to analyze data and draw meaningful conclusions, make informed decisions, and predict future outcomes. They are also essential in various fields such as economics, psychology, medicine, and engineering, where data analysis and prediction play a crucial role.

3. What are the main uses of statistics and probability?

The main uses of statistics and probability include:

  • Describing and summarizing data
  • Making inferences and predictions
  • Hypothesis testing
  • Quality control and process improvement
  • Risk assessment and management
  • Designing experiments
  • Market research and analysis

4. What are some common misconceptions about statistics and probability?

Some common misconceptions about statistics and probability include:

  • Assuming correlation implies causation
  • Believing that a small sample size is always representative of the population
  • Thinking that probability is only used in gambling or games
  • Assuming that a result is significant just because it is statistically significant
  • Believing that statistics can be used to prove or disprove anything

5. How can I improve my understanding and application of statistics and probability?

Improving your understanding and application of statistics and probability requires practice and a solid foundation in basic mathematical concepts. It is also helpful to learn about different statistical methods and their appropriate uses, as well as common pitfalls and biases to avoid. Additionally, staying updated on current research and advancements in the field can also enhance your understanding and application of statistics and probability.

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