Using the normal distribution and the central limit theorem, it is found that there is a 0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.
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.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For the population, the mean and the standard deviation are, respectively, given by [tex]\mu = 20, \sigma = 7[/tex].
For samples of n = 10, the standard error is given by:
[tex]s = \frac{7}{\sqrt{10}} = 2.2136[/tex]
The probability that the average water consumed by them is less than 18 ounces is the p-value of Z when X = 18, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18 - 20}{2.2136}[/tex]
Z = -0.9.
Z = -0.9 has a p-value of 0.18406.
0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
