Answer:
The minimum sample size to have this margin of error is n = 897.
Step-by-step explanation:
We have to estimate a parameter with a confidence interval. The confidence level is 95% and the margin of error is 0.5 days.
The population standard deviation is 7.64 days.
The critical value of z for a 95% confidence interval is z=1.96.
We have to calculate the minimum sample size.
To do that, we use the margin of error formula in function of n:
[tex]MOE=\dfrac{z\cdot \sigma}{\sqrt{n}}\\\\\\n=\left(\dfrac{z\cdot \sigma}{MOE}\right)^2=\left(\dfrac{1.96\cdot 7.64}{0.5}\right)^2=(29.95)^2=896.9\approx 897[/tex]
The minimum sample size to have this margin of error is n = 897.
