Answer:
The number of rainfalls required to be included in the sample is 97.
Step-by-step explanation:
The information provided is:
Error = E = 0.1
Standard deviation = σ = 0.5
1 - α = 0.95
α = 0.05
The error formula is:
[tex]E=z_{\alpha /2}\times\frac{\sigma}{\sqrt{n}}[/tex]
Compute the critical value as follows:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use the z-table for the critical value.
Compute the value of n as follows:
[tex]E=z_{\alpha /2}\times\frac{\sigma}{\sqrt{n}}\\0.1=1.96\times\frac{0.5}{\sqrt{n}} \\n=(\frac{1.96\times0.5}{0.1} )^{2}\\=96.04\\\approx97[/tex]
Thus, the number of rainfalls required to be included in the sample is 97.
