Answer:
0.1640 ≤ p ≤0.3532
Explanation:
Sample size (N) = 58 customers
Z-score for 90% interval (Z) = 1.645
The proportion of customers that received some cash back is given by:
[tex]p=\frac{15}{58}\\p=0.2586[/tex]
The confidence interval for the proportion of all depositors who ask for cash back is determined by the following relationship:
[tex]p\pm Z*\sqrt{\frac{p*(1-p)}{N}}[/tex]
Applying the given data:
[tex]0.2586\pm 1.645*\sqrt{\frac{0.2586*(1-0.2586)}{58}}\\0.2586\pm0.0946[/tex]
The upper and lower limits are:
[tex]L=0.2586-0.0946\\L =0.1640 \\L=0.2586-0.0946\\L = 0.3532[/tex]
Using a 90% confidence level, the interval for the proportion (p) is:
0.1640 ≤ p ≤0.3532
