Final answer:
The 95% confidence interval for the mean height of LSC-CF students is between 65.412 inches and 66.588 inches. This interval suggests that with 95% confidence, the true mean height of the student population is within these bounds.
Step-by-step explanation:
To calculate the 95% confidence interval for the mean height of LSC-CF students, we can use the formula for the confidence interval when the population standard deviation is unknown and the sample size is large (n ≥ 30). The formula is:
CI = μ ± (z * (S / √n)).
Here, μ is the sample mean height (66 inches), S is the sample standard deviation (3 inches), n is the sample size (100 students), and z is the z-score corresponding to the desired confidence level. For a 95% confidence interval, we commonly use a z-score of approximately 1.96.
Plugging the values into the formula, we get:
CI = 66 ± (1.96 * (3 / √100)).
Conducting the calculations:
CI = 66 ± (1.96 * 0.3),
CI = 66 ± 0.588,
which gives us a confidence interval from 65.412 to 66.588 inches.
The confidence interval indicates that we are 95% confident that the true mean height of all LSC-CF students lies between 65.412 inches and 66.588 inches.