Question 1184574
population mean is 14.4 years.
population standard deviation is 4.7 years.
sample size is 14.
degrees of freedom = 13


based on the guideline at <a href = "https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value" target = "_blank">https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value</a>, you would use the t-score for this problem.


standard error = standard deviation / square root of sample size = 4.7 / sqrt(14) =  1.25613.


t-score with 2% of the area under the normal distribution curve to the left of it with 13 degrees of freedom is -2.2816.


use the t-score formula to find the raw score.


t-score formula is t = (x - m) / s


that becomes:


-2.2816 = (x - 14.4) / 1.25613.


solve for x to get:


x = 1.25613 * -2.2816 + 14.4 = 11.534.


round to 1 decimal place to get 11.5.


that's your answer.