Answer :
Answer:
0.0228 = 2.28% probability that the mineral water supplied by the company will not satisfy the water demanded by its employees.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be 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.
n values from a normal distribution:
The mean is [tex]\mu*n[/tex] and the standard deviation is [tex]\sigma\sqrt{n}[/tex]
Normally distributed with mean 19 ounces and standard deviation 5 ounces.
This means that [tex]\mu = 19, \sigma = 5[/tex]
The company has 100 employees.
This means that for the mean consumption of all employees, we have that:
[tex]\mu = 19*100 = 1900[/tex]
[tex]\sigma = 5\sqrt{100} = 50[/tex]
Find the probability that the mineral water supplied by the company will not satisfy the water demanded by its employees.
Consumption higher than 2000 ounces, which is 1 subtracted by the pvalue of Z when X = 2000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2000 - 1900}{50}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that the mineral water supplied by the company will not satisfy the water demanded by its employees.