Respuesta :
Using the normal distribution, it is found that the probability that the association would observe 654 or less people who drink milk in the sample is of 0%.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].
For the binomial distribution, the parameters are given as follows:
n = 800, p = 0.87.
Hence, the mean and the standard deviation of the approximation are given by:
- [tex]\mu = np = 800 \times 0.87 = 696[/tex]
- [tex]\sigma = \sqrt{np(1-p)} = \sqrt{80 \times 0.87 \times 0.13} = 9.5121[/tex].
The probability that the association would observe 654 or less people who drink milk in the sample, using continuity correction, is [tex]P(X \leq 654.5)[/tex], which is the p-value of Z when X = 654.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{654.5 - 696}{9.5121}[/tex]
Z = -4.36
Z = -4.36 has a p-value of 0.
0% probability that the association would observe 654 or less people who drink milk in the sample.
More can be learned about the normal distribution at https://brainly.com/question/20909419
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