Respuesta :
Answer:
0.5793 = 57.93% probability that the household uses 480 gallons of water or less per month
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 470 gallons and standard deviation of 50 gallons.
This means that [tex]\mu = 470, \sigma = 50[/tex]
What is the probability that the household uses 480 gallons of water or less per month?
This is the pvalue of Z when X = 480. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{480 - 470}{50}[/tex]
[tex]Z = 0.2[/tex]
[tex]Z = 0.2[/tex] has a pvalue of 0.5793
0.5793 = 57.93% probability that the household uses 480 gallons of water or less per month
