Answer :
Final answer:
The correct option of the given statement "Assume that the weights of students in U.O.P. follow normal distribution with mean 65kg and variance 4kg. We choose 9 persons randomly, find the probability that their sample mean is at least 67kg?" is a. 0.0013.
Explanation:
To find the probability that the sample mean is at least 67kg, we need to calculate the probability of selecting a sample mean that is greater than or equal to 67kg. Since the population follows a normal distribution, the distribution of the sample means will also follow a normal distribution.
The mean of the sample means will be equal to the population mean, which is 65kg. The standard deviation of the sample means, also known as the standard error, can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, since the sample size is 9, the standard error will be √(4/9) = 2/3.
Now we can calculate the z-score of 67kg, which is the number of standard deviations the sample mean is from the population mean. The z-score can be calculated as (67 - 65) / (2/3) = 3.
Finally, we can find the probability of selecting a sample mean greater than or equal to 67kg by looking up the z-score in the standard normal distribution table. The probability is given by 1 - P(Z < 3), which is approximately 1 - 0.9987 = 0.0013. Therefore, the correct answer is a. 0.0013.
Learn more about the topic of Probability here: brainly.com/question/32117953
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