Answer: 0.1632
Step-by-step explanation:
Given : The proportions of multiple samples of registered voters who vote are normally distributed .
Mean proportion : [tex]\mu=0.38[/tex]
Standard deviation : [tex]\sigma: 0.0485[/tex]
Let x be the random variable that represents the proportion of registered
voters.
To find : The probability that a sample chosen at random has a proportion of registered voters who vote between 0.37 and 0.39.
We first find z-score corresponds 0.37 and 0.39.
Formula for z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 0.37
[tex]z=\dfrac{0.37-0.38}{0.0485}\approx-0.206[/tex]
For x= 0.39
[tex]z=\dfrac{0.39-0.38}{0.0485}\approx0.206[/tex]
By using the standard normal table, the required probability will be :_
[tex]P(0.37<x<0.39)=P(-0.206<z<0.206)\\\\=0.5816045-0.4183955=0.163209\approx0.1632[/tex]
Hence, the probability that a sample chosen at random has a proportion of registered voters who vote between 0.37 and 0.39 = 0.1632
