Answer: 1692
Step-by-step explanation:
Formula to find the sample size :
[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex]
Given : Confidence level : [tex](1-\alpha)=0.90[/tex]
⇒ significance level =[tex]\alpha= 0.10[/tex]
z-value for 90% confidence interval (using z-table)=[tex]z_{\alpha/2}=1.645[/tex]
Prior estimate of the population proportion (p) of customers who keep up with regular vehicle maintenance is unknown.
Let we take p= 0.5
Margin of error : E= 2%=0.02
Now, the required sample size will be :
[tex]n=0.5(1-0.5)(\dfrac{1.645}{0.02})^2[/tex]
Simplify , we get
[tex]n=(0.25)(6765.0625)=1691.265625\approx1692[/tex]
Hence, the required sample size = 1692
