Final answer:
To calculate the probability that the mean height for a sample of 55 women in a country aged 20-29 is greater than 65 inches, we can use the Central Limit Theorem.
Step-by-step explanation:
To answer this question, we can use the Central Limit Theorem. The Central Limit Theorem states that for a large enough sample size, the distribution of the sample mean will be approximately normal, regardless of the shape of the population.
In this case, the population standard deviation is known to be 2.61 inches, so we can calculate the standard error of the mean by dividing the population standard deviation by the square root of the sample size.
So, the standard error of the mean is 2.61 / sqrt(55) = 0.35 inches. Now, we can calculate the z-score for a sample mean of 65 inches using the formula: z = (sample mean - population mean) / standard error of the mean. Plugging in the values, we get z = (65 - 64.1) / 0.35 = 2.57.
Finally, we can use a normal distribution table or a calculator to find the probability that a z-score is greater than 2.57. This probability represents the probability that the mean height for the sample is greater than 65 inches.
A z-score of 2.57 corresponds to a probability of approximately 0.9951, or 99.51%.