Answer :
we need to find the probability that the mean of a sample of 50 individuals will be greater than 200 pounds. The probability that the mean of the sample will be greater than 200 pounds is approximately 0.0985, which corresponds to option B.
To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough. In this case, since the sample size is 50, we can assume that the sample mean follows a normal distribution.
We can calculate the z-score using the formula:
z = (x - μ) / (σ / sqrt(n))
where x is the desired value (200 pounds), μ is the population mean (196 pounds), σ is the population standard deviation (22 pounds), and n is the sample size (50).
After calculating the z-score, we can then find the probability using a standard normal distribution table or calculator. The probability that the mean of the sample will be greater than 200 pounds is approximately 0.0985, which corresponds to option B.
To know more about Central Limit Theorem here: brainly.com/question/898534
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