B) Explain why your answer to part (a) is an estimate.

(a) Y = 129.3x (b) It is an estimate as it may not be a true reflection of a student's height

Step-by-step explanation:

(a) Estimate of the mean height is the sum of the heights of all the students divided by the total number of students.

The question however needs more information for its estimation as 129.3cm is representative and may be the mean height but it was not stated.

However, assuming it is the mean height,

Let the total number of students be x

while Y is the sum of all individual student heights

Mathematically, mean = Y/x

Therefore 129.3 = Y/ x

implying that Y = 129.3x

(b) It is an estimate because computation of the mean gives an average which may not be an exact value. For example, the mean here is 129.3 whereas there will be many heights greater than that and some lesser than that and obviously, there may be no student with height of 129.3 hence it is an estimate.