A Statistics class is estimating the mean height of all female students at their college. They collect a random sample of 36 female students and measure their heights. The mean of the sample is 65.3 inches. The standard deviation is 5.2 inches. What is the 90% confidence interval for the mean height of all female students in their school? Assume that the distribution of individual female heights at this school is approximately normal? (56.5, 74.1) (63.6, 67.0) (63.8, 66.8) (63.9, 66.7) Question 3
Accepted Solution
A:
Answer: Fourth option is correct.Step-by-step explanation:Since we have given that Mean of sample = 65.3Standard deviation = 5.2We need to find the 90% confidence interval for the mean.So, z = 1.64And the interval would be [tex]\bar{x}\pm z\times \dfrac{\sigma}{\sqrt{n}}\\\\=65.3\pm 1.64\times \dfrac{5.2}{\sqrt{36}}\\\\=65.3\pm 1.42\\\\=(65.3-1.42,65.3+1.42)\\\\=(63.88,66.72)\\\\=(63.9,66.7)[/tex]Hence, Fourth option is correct.