How Many More Parcels Must Be Weighed?

A courier company weighs parcels to estimate the mean parcel weight $\mu$ at one depot. From years of records, the population standard deviation is known to be

$\sigma = 4.5 \text{ kg}$

A pilot study has already weighed 36 randomly selected parcels.

Management now insists that the estimate be precise enough that the standard error of the sample mean satisfies

$SE(\bar{x}) = \frac{\sigma}{\sqrt{n}} \le 0.25 \text{ kg}$

Parcels are still being sampled independently and at random, and the 36 already weighed count towards the total.

How many additional parcels must be weighed, on top of the 36 already done, to reach that precision?

Give your answer as a whole number of parcels, rounding up to the nearest whole parcel if necessary.