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Answer :
Final answer:
To find the probability that the sample mean is greater than or equal to 108.8, we convert the sample mean to a z-score, which gives us the number of standard deviations this score is from the mean. The score of 108.8 is 2.16 standard deviations above the mean, thus the probability of obtaining this or a higher score is approximately 1.5%.
Explanation:
To find the probability that the sample mean is greater than or equal to 108.8, we first need to convert the sample mean to a z-score using the formula: z = (M - u) / (o / √n).
Here, M is the sample mean (100.8), u is the population mean (100), o is the population standard deviation (16), and n is the sample size (9).
Before we can use the z-score formula, we need to adjust the standard deviation as well. Since we're given the sample standard deviation (12.13), we need to estimate the population standard deviation. In most cases, the sample standard deviation is a good approximation of the population standard deviation, so for the purpose of this question, we'll use 12.13 as our value for o.
Using these values in the z-score formula, we get z = (108.8 - 100) / (12.13 / √9) = 2.16.
This indicates that the score of 108.8 is 2.16 standard deviations above the mean. In a standard normal distribution, approximately 98.6% of the scores fall within 2.16 standard deviations of the mean. Thus, the probability of obtaining a mean of 108.8 or higher is very small, approximately 0.015 or 1.5%.
Learn more about Z-score Calculation here:
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