Answer:
190
Step-by-step explanation:
Data provided in the question:
Confidence level = 99%
Therefore,
α = 1% = 0.01
[ from standard normal table ]
z-value for [tex]z_{\frac{\alpha}{2}}= z_{\frac{0.01}{2}}=[/tex] = 2.58
Margin of error, E = $0.06
Standard deviation, σ = $0.32
Now,
n = [tex](\frac{z_{0.005}\sigma}{E})^2[/tex]
Here,
n is the sample size (or the minimum number of gas stations )
on substituting the respective values, we get
= [tex](\frac{z_{0.005}\sigma}{E})^2[/tex]
= [tex](\frac{2.58\times0.32}{0.06})^2[/tex]
= 13.76²
= 189.3376 ≈ 190
Hence,
minimum number of gas stations that she should include in her sample is 190
