Answer :
Final answer:
To calculate the probability that the mean of a sample is less than 200 pounds, you would use the Z-test formula for a population mean, Z = (X - μ) / (σ/√n), and look up the resulting Z-score in a standard normal Z-table or use an online calculator.
Explanation:
The subject of this question is statistics, and more specifically, how to calculate the probability of a sample mean using information about the mean and standard deviation of a population.
In this case, the population mean is the average number of pounds of red meat consumed per person per year, which is 196 pounds. The standard deviation is 22 pounds, and we want to find the probability that the mean of a randomly selected sample of 50 individuals is less than 200 pounds.
The formula for calculating the probability of a sample mean is Z = (X - μ) / (σ/√n), where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plug in the given numbers: Z = (200 - 196) / (22/√50). You'll get a Z-score, which you can then look up in a standard normal Z-table (or use an online calculator) to find the corresponding probability.
This problem is an example of a Z-test for a population mean, which is a common method used in statistics to test hypotheses about population means.
Learn more about Z-test for a popultation mean here:
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