Answer: C) 133
Step-by-step explanation:
The formula to find the sample size is given by :-
[tex]n=(\dfrac{z^*\cdot\sigma}{E})^2[/tex]
, where z* = Critical z-value
[tex]\sigma[/tex] = Population standard deviation for prior study.
E= Margin of error.
As per given , we have
[tex]\sigma=$35[/tex]
E= 5
The critical z-value for 90% confidence level is 1.645.
Substitute al;l the value sin the above formula , we get
[tex]n=(\dfrac{1.645\times 35}{5})^2[/tex]
[tex]n=(\dfrac{57.575}{5})^2[/tex]
[tex]n=(11.515)^2[/tex]
[tex]n=132.595225\approx133[/tex]
Hence, the minimum sample size needed is 133.
Thus , the correct answer is : C) 133
