Answer: 48
Step-by-step explanation:
Formula to find the minimum sample size :-
[tex]n=(\dfrac{z^*\cdot \sigma}{E})^2[/tex]
, where [tex]\sigma[/tex] = population standard deviation
z* = Critical value.
E = Margin of error .
As per given , we have
[tex]\sigma=8.4[/tex]
E=2 units
Confidence level= 90%
By z-vale table , the critical value for 90% confidence = [tex]z^*=1.645[/tex]
Then, the minimum sample size would be :-
[tex]n=(\dfrac{(1.645)\cdot (8.4)}{2})^2\\\\=(6.909)^2\\\\=47.734281\approx48[/tex]
Hence, the minimum sample size needed = 48
