Answer:
The minimum sample size is 239.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Z-table as such z has a p-value of
.
That is z with a pvalue of
, so Z = 2.575.
Now, find the margin of error M as such

In which
is the standard deviation of the population and n is the size of the sample.
Population standard deviation is equal to 1.5
This means that 
Margin of error of 0.25
This means that 
What's the minimum size of the sample?






Rounding up:
The minimum sample size is 239.