Answer:
The average number of days is more than 43% from the past 8 years is 43.15 days and it is less than Sample mean of 47 for 20 samples
Explanation:
From the data
Population mean = μ=43 days
Population variance=[tex]\sigma^2[/tex]=196
[tex]\sigma=\sqrt{196}=14[/tex]
Sample size n=20
Sample mean [tex]\bar{x}[/tex]=47
Part a:
Using values from the reference question found online.
Given α=43%
α=0.43
At 1-α=0.57
[tex]z_{\alpha}[/tex] from the table yields 0.18
Now the value is given as
[tex]\bar{x}=\mu+z_{\alpha}\sqrt{\frac{\sigma}{n}}\\\bar{x}=43+0.18\sqrt{\frac{14}{20}}\\\bar{x}=43.15 days[/tex]
Part b:
Sample mean of 47 for 20 samples is more than 43% of the days from last 8 years.
