Respuesta :
Answer:
100% probability that Joe Biden wins Yolo county
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For a proportion q in a sample of size n, the mean is [tex]\mu = q[/tex] and the standard deviation is [tex]\sigma = \frac{q(1-q)}{\sqrt{n}}[/tex]
In this problem, we have that:
[tex]q = 0.51, n = 1000000[/tex]
So
[tex]\sigma = \sqrt{\frac{0.51*0.49}{\sqrt{1000000}} = 0.0005[/tex]
What is the probability that Joe Biden wins Yolo county?
This is the probability that he gets more than 50% = 0.5 of the votes, so it is 1 subtracted by the pvalue of Z when X = 0.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.5 - 0.51}{0.0005}[/tex]
[tex]Z = -20[/tex]
[tex]Z = -20[/tex] has a pvalue of 0
1 - 0 = 1
100% probability that Joe Biden wins Yolo county
Answer:
100% probability that Joe Biden wins Yolo county
Step-by-step explanation:
